Question

week 7 review. divide using rectangle division. select the answer from the list below. (5x³ - 26x² - 64x - 22)÷(5x + 4). a) x² - 6x - 10 + 13/(5x + 4). b) x² - 6x - 7 + 10/(5x + 4). c) x² - 6x - 8 + 10/(5x + 4). d) x² - 6x - 10 + 6/(5x + 4).

Explanation:

Step1: Perform polynomial long - division

We divide the polynomial \(5x^{3}-26x^{2}-64x - 22\) by \(5x + 4\).
First, divide the leading term of the dividend \(5x^{3}\) by the leading term of the divisor \(5x\) to get \(x^{2}\).
Multiply \(5x + 4\) by \(x^{2}\) gives \(5x^{3}+4x^{2}\).
Subtract this from the dividend: \((5x^{3}-26x^{2}-64x - 22)-(5x^{3}+4x^{2})=-30x^{2}-64x - 22\).

Step2: Continue the long - division

Divide the leading term of \(-30x^{2}\) (the new dividend) by the leading term of \(5x\) to get \(- 6x\).
Multiply \(5x + 4\) by \(-6x\) gives \(-30x^{2}-24x\).
Subtract this from \(-30x^{2}-64x - 22\): \((-30x^{2}-64x - 22)-(-30x^{2}-24x)=-40x - 22\).

Step3: Final step of long - division

Divide the leading term of \(-40x\) by the leading term of \(5x\) to get \(-8\).
Multiply \(5x + 4\) by \(-8\) gives \(-40x-32\).
Subtract this from \(-40x - 22\): \((-40x - 22)-(-40x-32)=10\).

The quotient is \(x^{2}-6x - 8\) and the remainder is \(10\). So the result of the division is \(x^{2}-6x - 8+\frac{10}{5x + 4}\).

Answer:

C. \(x^{2}-6x - 8+\frac{10}{5x + 4}\)