Question

Let the function P be defined by P(x) = x³ + 7x² - 26x - 72, where (x+9) is a factor. To rewrite the function as the product of two factors, long division was used, but an error was made. What is the correct factorization of the function P(x)?

A) P(x) = (x + 9)(x² + 16x + 118)
B) P(x) = (x + 9)(x² + 16x - 118)
C) P(x) = (x + 9)(x² + 16x - 144)
D) P(x) = (x + 9)(x² + 16x - 1062)

Answer 1

The correct factorization of the function P(x) = x³ + 7x² - 26x - 72 is (x + 9)(x² + 16x + 118). Hence the correct answer is option A

Step-by-step explanation:

The correct factorization of the function P(x) = x³ + 7x² - 26x - 72 is A) P(x) = (x + 9)(x² + 16x + 118).

To determine the correct factorization, let's first divide P(x) by (x + 9) using long division:

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x² + 16x + 118 | x³ + 7x² - 26x - 72

- (x³ + 9x²)

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-2x² - 26x

- (-2x² - 18x)

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-8x - 72

- (-8x - 72)

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0

Since the remainder is 0, we have successfully divided P(x) by (x + 9). Therefore, the correct factorization is A) P(x) = (x + 9)(x² + 16x + 118).