Question

let the function p be defined by p(x) = x^3 + 10x^2 - 23x - 132 where (x + 11) is a factor. to rewrite the function as the product of two factors, long division was used, but an error was made:

Answer 1

In long division a polynomial is divided by another polynomial with a lower degree

• The two factors are; (x² - x - 12) and (x + 11)

Reason:

The given function is presented as follows;

x³ + 10·x² - 23·x - 132

A factor of the function is (x + 11)

By long division, we have;

Quotient; x² - x - 12

${}$                (x³ + 10·x² - 23·x - 132) ÷ (x + 11)

${}$                 x³ + 11·x²

${}$                         -x² - 23·x - 132

${}$                         -x² - 11·x

${}$                               -12·x - 132

${}$                               -12·x - 132

${}$                                            0

Therefor, we have the two factors, are (x² - x - 12) and (x + 11)

Where;

(x² - x - 12) = (x - 4)·(x + 3)

Therefore, we have;

(x² - x - 12) × (x + 11) = x³ + 10·x² - 23·x - 132

Learn more about long division here;

brainly.com/question/12562913