Is (x+7) a factor of f(x)= x^3-3x^2+2x-8

Since f(-7) ≠ 0, hence (x+7) is not a factor of f(x)= x³-3x²+2x-8

Polynomial is an expression involving the operations of addition, subtraction, multiplication of variables.

Types of polynomials are quadratic, linear, cubic and so on.

The factor theorem states that; when f(k) = 0, then (x – k) is a factor of f(x).

To determine if (x+7) a factor of f(x)= x^3-3x^2+2x-8, we:

x + 7 = 0

x = -7

f(-7) = (-7)³ - 3(-7)² + 2(-7) - 8 = -512

Since f(-7) ≠ 0, hence (x+7) is not a factor of f(x)= x³-3x²+2x-8

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Step-by-step explanation:

Use synthetic division to answer this.  If the remainder is zero, then we can safely assume the divisor (x + 7) is a factor of the polynomial f(x)= x^3-3x^2+2x-8.

We use -7 as the divisor in synth. div.  This comes from the factor (x + 7):

-7   /    1    3     2     -8

               -7   28  -210

         1      -4   30   -218

Here, the remainder is -218, not zero, so no, (x+7) is not a factor of f(x)= x^3-3x^2+2x-8.