Question

Which expression is a factor of this polynomial?

Answer 1

The factor is the solution of zeros of the equation and x + 2 making it zero therefore x + 2 will be the solution of the given polynomial so option (B) will be correct.

What are the roots of an equation?

Roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.

Given the polynomial,

x³ + 2x² - 9x - 18

A factor is consist of a solution of zeros of any polynomial.

For example;

x² + 5x + 6 = 0

x(x + 2) + 3(x + 2) = 0

(x + 3)(x + 2) = 0

Here x + 3 and x + 2 are factor and solution is x = -3 and -2

Similarly,

x³ + 2x² - 9x - 18 = 0

The factor must be the solution to this.

By cross-checking option

Option (A) x + 1 = 0 → x = -1

Keeping x = -1

(-1)³ + 2(-1)² - 9(-1) - 18 = -8 ≠ 0 so it is not the factor.

Option (B) (x + 2) = 0 → x = -2

(-2)³ + 2(-2)² - 9(-2) - 18

-8 + 8 + 18 - 18 = 0 = 0 so it will be factor of the polynomial.

Hence " x + 2 will be the solution of the given polynomial".

To learn more about the roots of an equation,

brainly.com/question/12029673

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