Use the Remainder Theorem to determine whether or not x + 3 is a divisor of p (x) = 2x^3 + 4x^2 - 2x + 12

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The remainder when the polynomial p(x) = 2x³ + 4x² - 2x + 12 is divided by x + 3 is -6.

A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables.

The remainder theorem states that for a polynomial, f(x) divided by a linear polynomial , x - a, the remainder is equal to f(a).

Given the polynomial; p(x) = 2x³ + 4x² - 2x + 12, since it is divided by x + 3, hence:

x + 3 = 0

x = -3

p(-3) = 2(-3)³ + 4(-3)² - 2(-3) + 12 = -6

Hence the remainder when the polynomial p(x) = 2x³ + 4x² - 2x + 12 is divided by x + 3 is -6.

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