Use the factor theorem to determine whether or not the first polynomial is a factor of the second
Answers
Answer/Step-by-step explanation:
Based on the factor theorem, a polynomial, x - a, is said to be a factor of another polynomial, f(x), if an only if f(a) = 0.
Using this theorem, let's determine whether each of the given first polynomial, is a factor of the second polynomial.
1. x - 1; x² + 2x + 5
By the factor theorem, x - 1 will be a factor of f(x) = x² + 2x + 5, if and only if f(1) = 0.
f(1) = 1² + 2(1) + 5
= 1 + 2 + 5
= 8
Since f(1) ≠ 0, therefore the first polynomial, x - 1, is NOT a factor of the second polynomial, x² + 2x + 5.
2. x + 1; x³ - x - 2
By the factor theorem, x + 1 will be a factor of f(x) = x³ - x - 2, if and only if f(-1) = 0.
f(1) = -1³ - (-1) - 2
= -1 + 1 - 2
= -2
Since f(-1) ≠ 0, therefore the first polynomial, x + 1, is NOT a factor of the second polynomial, x³ - x - 2.
3. x - 4; 2x³ - 9x² + 9x - 20
By the factor theorem, x - 4 will be a factor of f(x) = 2x³ - 9x² + 9x - 20, if and only if f(4) = 0.
f(4) = 2(4)³ - 9(4)² + 9(4) - 20
= 128 - 144 + 36 - 20
= 0
Since f(4) = 0, therefore the first polynomial, x + 4, is a factor of the second polynomial, 2x³ - 9x² + 9x - 20.
4. a - 1; a³ - 2a² + a - 2
By the factor theorem, a - 1 will be a factor of f(a) = a³ - 2a² + a - 2, if and only if f(1) = 0.
f(1) = 1³ - 2(1)² + 1 - 2
= 1 - 2 + 1 - 2
= -2
Since f(1) ≠ 0, therefore the first polynomial, a - 1, is NOT a factor of the second polynomial, a³ - 2a² + a - 2.
5. y + 3; 2y³ + y² - 13y + 6
By the factor theorem, y + 3 will be a factor of f(y) = 2y³ + y² - 13y + 6, if and only if f(-3) = 0.
f(-3) = 2(-3)³ + (-3)² - 13(-3) + 6
= -54 + 9 + 39 + 6
= 0
Since f(-3) = 0, therefore the first polynomial, y + 3, is a factor of the second polynomial, 2y³ + y² - 13y + 6.
Related Questions
8,900 incoming freshman to a university take an entrance exam, with the top 10% being offered admission to the university's honors program. The average test score is 78%, with a standard deviation of 11%. Use a calculator to find what the student must score to be invited to join the honors program if only 65 scores are looked at to determine the honors admissions requirement.
Answers
Answer:
The student must score 79.75% to be invited to join the honors program.
Step-by-step explanation:
Let X denote the score of a freshman in the entrance exam.
It is provided that the average test score is 78%, with a standard deviation of 11%.
It is provided that the top 10% being offered admission to the university's honors program.
Let x denote the score eligible for being offered admission to the university's honors program.
Then, P (X ≤ x) = 0.90.
Then P (Z < z) = 0.90.
The corresponding z-score is, 1.28.
*Use a z-table.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n}}\\\\1.28=\frac{x-78}{11/\sqrt{65}}\\\\x=78+(1.28\times \frac{11}{\sqrt{65}})\\\\x=79.75\%[/tex]
Thus, the student must score 79.75% to be invited to join the honors program.
The equations y = tan^2 (x) and y = 1 are graphed below. According to the graphwhich of the following is part the solution to the trigonometric inequality tan^2 (x) < 1 over the interval 0 <= x <= 2pi radians?
Answers
Answer: a
Step-by-step explanation:
just took test edg2020
The part of the solution of the equation that lies in the solution region of the inequality is x = π/6, the correct option is A.
What is an Inequality?An Inequality is a statement that is formed when two expressions are joined using an inequality operator.
The equation is
y = tan²x
y = 1
the inequalities are
tan²x < 1 ( 0≤ x ≤ 2π)
The graph of the system of equations and the inequality is plotted, and attached with the answer.
The answer can be seen as x = π/6.
To know more about Inequality
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Jane needs open-topped boxes to store her excess inventory at year's end. She purchases large
rectangles of thick cardboard with a length of 12 inches and width of 8 inches to make the boxes.
She is interested in maximizing the volume of the boxes and wants to know what size squares to
cut out at each corner of the cardboard (which will allow the corners to be folded up to form the
box) to do this. What is the maximum volume?
Answers
Answer:
x = 1,6 in ( the side of the corner squares )
V(max) = 67,58 in³
Step-by-step explanation:
The cardboard is:
L = 12 in w = 8 in
Let´s call "x" the side of the square from the corner:
Then the sides of the base of the open box are:
( L - 2*x ) and ( w - 2*x ) and x is the height
( 12 - 2*x ) and ( w - 2*x )
V(ob) = (L - 2*x ) * ( - 2*x ) * x
Wich is a function of x
V(x) = [( 12 - 2*x ) * ( 8 - 2*x ) ]*x
V(x) = ( 96 - 24*x - 16*x + 4*x²) * x
V(x) = 96*x - 40*x² + 4*x³
Tacking derivatives on both sides of the equation
V´(x) = 12*x² - 80*x + 96
V´(x) = 0 12*x² - 80*x + 96 = 0
Solving for x
x₁,₂ = 80 ± √ 6400 - 4608 / 24
x₁,₂ = 80 ± 42,33 / 24
x₁ = 5,10 We dismiss this solution since 2*x becomes 2*5,10 = 10,20
ant this value is bigger than 8 inches
x₂ = 1,60 in
Therefore dimensions of the box
a = 12 - 2*x ; a = 12 - 3,20 ; a = 8,8 in
b = 8 - 2*x ; b = 8 - 3,20 ; b = 4,80 in
And the volume of the open box is:
V(max) = 8,8*4,8*1,6
V(max) = 67,58 in³
How do we Know that is the maximun value for V?
We find V´´(x) = 24*x - 80 for x = 1,6 is negative ( V´´(x) = - 41,6 therefore V (x) has a local maximun for a value of x = 1,6
What is the quotient between 215÷9
Answers
215/9
= 23.888888........
It is written as shown in the picture
Evan's favourite hobby is origami. He plans to make 100 paper cranes to hang from the ceiling of his bedroom. Yesterday, he made 28 paper cranes in 4 hours. Today, he made 21 paper cranes at the same rate.
How long did Evan spend making paper cranes today?
Answers
Answer:
it took him 3 hours
Step-by-step explanation:
28 divideed by 4= 7
21divided by 7=3
Given f(x)=2x+5 find f(3)
answer choices are:
1. ) 28
2.) -28
3.) 11
4.) 6x+5
5.) 5
Answers
Answer:
3.) 11
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASStep-by-step explanation:
Step 1: Define
f(x) = 2x + 5
f(3) is x = 3
Step 2: Solve
Substitute: f(3) = 2(3) + 5Multiply: f(3) = 6 + 5Add: f(3) = 11Graph a line with a slope of 4 that contains the point (3,0).
Answers
Hi there!
Recall that slope-intercept form is:
y = mx + b
Where m = slope
In this instance, we are given a slope of 4, therefore:
y = 4x + b
Substitute in the x and y coordinates of the point given:
0 = 4(3) + b
0 = 12 + b
Subtract 12 from both sides:
-12 = b
Therefore, the equation would be:
y = 4x - 12
Graph the equation by finding x and y values or using a calculator:
x = 0, y = 4(0) - 12 = 12 (0, 12)
x = 1, y = 4(1) - 12 = -8 (1, -8)
x = 2, y = 4(2) - 12 = -4 (2, -4)
x = 3, y = 4(3) - 12 = 0 (3, 0)
And so forth:
To graph a line passing through a point (3, 0) and slope 4, we will find the equation of the line first.
Since, equation of a line passing through a point (h, k) and slope 'm' is given by,
y - k = m(x - h)
Therefore, equation of a line passing through (3, 0) and slope 4 will be,
y - 0 = 4(x - 3)
y = 4x - 12
For y-intercept put x = 0 in the equation,
y = 4(0) - 12
y = -12
For x-intercept put y = 0 in the equation,
0 = 4x - 12
x = 3
Therefore, line will intersect x-axis at (3, 0) and y-axis at (0, -12).
By joining these points we can find the graph of the line passing through (3, 0) and having slope = 4.
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Use the distributive property to remove the parentheses.
2x+(6x2-9)
Simplify your answer as much as possible.
Answers
After removing the parentheses using the distributive property, the expression [tex]2x^4 (6x^2 - 9)[/tex] simplifies to [tex]12x^6 - 18x^4.[/tex]
We have,
To remove the parentheses using the distributive property, we need to multiply each term inside the parentheses by the term outside the parentheses.
Applying the distributive property to the expression [tex]2x^4 (6x^2 - 9),[/tex] we have:
[tex]2x^4 * 6x^2 - 2x^4 * 9[/tex]
Multiplying the terms:
[tex]12x^6 - 18x^4[/tex]
Therefore,
After removing the parentheses using the distributive property, the expression [tex]2x^4 (6x^2 - 9)[/tex] simplifies to [tex]12x^6 - 18x^4.[/tex]
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[PICTURE] please answer all questions 1-5 ASAP thanks! FOR 20 PTS!!
Answers
Answer:
bellnshaped i think
Step-by-step explanation:
Divide 7560 in the ratio 4 : 5
Answers
Answer:
3360 4200
Step-by-step explanation:
Solve the word problem using a proportion. Danny, who was 6 ft tall, cast a 15 ft shadow. The building he was standing next to cast a 35 ft shadow. How tall was the building? 30 ft, 70 ft, or 14 ft?
Answers
Answer: 14 feet
Step-by-step explanation:
Answer:
14 feet
Step-by-step explanation:
Look at the shaded products. All of the products are the same number. What is true about the pattern?
One of the factors is always 1. When you multiply a number by 1, the product is that number.
One of the factors is always 1. When you multiply a number by 1, the answer is always 1.
One of the factors is always 0. When you multiply a number by 0, the product is that number.
One of the factors is always 0. When you multiply a number by 0, the product is always 0.
Answers
Answer:
The Answer is One of the factors is always 0. When you multiply a number by 0, the product is always 0.
Saleh can jog 2 3/7 miles in 6/11 hour. Find his average speed in miles per hour.
Answers
Answer:
3.73
Step-by-step explanation:
I NEED ANSWER ASAP PLEASE
NEED HELP
Answers
X to the second power plus 3x - 4=6
Answers
Answer:
answer is 2
Step-by-step explanation:
Answer:
x^2+3x-4=6
Step-by-step explanation:
first you add the x
Raia purchases a new car for $32,000 and
finances it with a 6-year simple interest
loan at a rate of 4.25%. What are Raia’s
monthly car payments?
Answers
2. Which relation below is NOT a function?
A. {(-2, 4), (1,3), (0,4)}
B. {(5,5), (4,4), (3,3) }
C. {(-4,0), (-7,0), (11, 0)}
D. {(1,4), (2,5) (1,7)}
Answers
C is the answer to that question i think
Answer:
b
Step-by-step explanation:
The answer is B because different X values cannot have the same y values. For example in A the x values, -2 and 0, have the same y value 4. That's not possible.
Although C also has a similar problem ALL of the X values have the same y value meaning that the function is an undefined function which is still a type of function. Its basically a function where all the y values are the same.
c. What is the major drawback of using the recursive rule?
Answers
Answer:
Use of recursion in an algorithm has both advantages and disadvantages. The main advantage is usually the simplicity of instructions. The main disadvantage is that the memory usage of recursive algorithms may grow very quickly, rendering them impractical for larger instances.
Answer:
uses more memory
recursion can be slow
Determine whether the two lines are parallel, perpendicular, coinciding, or only intersecting. y = - 2x + 7 6x + 3y = 1 Choose the correct answer below. coinciding O only intersecting O parallel O perpendicular
Answers
Answer:
Intersecting
Step-by-step explanation:
Can someone pls help me this it’s due in an hour but I can’t figure it out
Answers
Answer: I do believe that it is that the smooth shape is the dominate and the wrinkled is the resistive.
Step-by-step explanation:
Please answer this correctly without making mistakes
Answers
Answer:
4 dollars per pound
Step-by-step explanation:
3 x 4 =12
read the the following question
Answers
Answer:
11 (answer c)
Step-by-step explanation:
you need to find LCD and then combine
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[tex] \frac{7}{8} \div \frac{1}{8} + {2}^{2} = \\ [/tex]
[tex]( \frac{7}{8} \times 8) + {2}^{2} = \\ [/tex]
[tex]7 + 4 = 11[/tex]
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Lisa and Rachel want to determine their muscular endurance, but they don't have access to a gym or any weight-lifting equipment. What can they use?
A.
maxing out method
B.
percent of 1 RM method
C.
calisthenic method
D.
absolute method
Answers
Answer:
C- calisthenic method
Step-by-step explanation:
In the absence of the weight-lifting equipment, it is also possible to measure the muscular endurance by the use of the calisthenic method.
What is muscular endurance?The term muscular endurance has to do with the ability of a muscle to undergo a strenous activity repeatedly without being fatigued. It is common to measure muscular endurance by the use of weight-lifting equipments.
In the absence of the weight-lifting equipment, it is also possible to measure the muscular endurance by the use of the calisthenic method.
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Help, Ill give extra points too!
Answers
Answer:
(-6,-18) & (2,6) -----------> 3
(12,6) & (-4,-2) -----------> [tex]\frac{1}{2}[/tex]
(5,-19) & (6,-23) ----------> -4
(3,4) & (3,9) ---------------> unidentified
(1,-10) & (2,-15) -----------> -5
(-1,8) & (3,8) ---------------> 0
(0,0) & (21,14) -------------> [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Use this formula to find all of these slopes.
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
what is the value of the digit in the tens place? 6,423
Answers
Answer: 20 :)
Step-by-step explanation:
Select the story problem that this division problem represents. 3/4 / 1/5. Please help I will give brainliest, thanks!
Answers
Answer:
The answer is b
Step-by-step explanation:
To find the length of the mosaic, we need to use the area divided by width which is 3/4 / 1/3
Find the equation of the line parallel to y=3x+5 that passes through (0,4) y=3x+4
Answers
∠10 and angle _____ are complementary angles.?
a.) ∠9 I
b.)∠11 O
Answers
Answer:
9
Step-by-step explanation:
they add up to 90 degrees
Answer: B
Step-by-step explanation:
HAVE A BLESSED DAY!!!!!!
I didn't grasp this topic too well. can someone help me?
Answers
Answer:
2 hours
Step-by-step explanation:
I'm pretty sure its 2 hrs. If she did not take any breaks, she would have made it in 2 hrs due to her taking a 2 hr break. If its not 2 hours, its 3. But I am 99% sure its 2 hrs.
find the missing value for each of the following 3 questions
1. 5% of 60 is _____
2. 40% of 500 is _____
3. 75% of 60 is ______
Answers
Answer:
1. 3
2. 200
3. 45
Step-by-step explanation:
