Question

Let the function T(x) be defined by T(x)=x³+7x²-26x-72. jake used long division to find the quotient of T(x) and (x+9):

a) 3x² - 16x - 80
b) 2x³ + 8x² - 35x - 93
c) x² - 2x - 8
d) 4x³ + 5x² - 31x - 63

Answer 1

Jake's quotient of T(x) divided by (x+9) is option (c), which is x² - 2x - 8. This finding is the result of performing polynomial long division or synthetic division correctly.

Step-by-step explanation:

The student has asked about the quotient of the polynomial T(x) when it is divided by (x+9).

To assist Jake in verifying his answer, we must use polynomial long division or synthetic division to divide the polynomial T(x) = x³ + 7x² - 26x - 72 by x + 9. The correct quotient will have a degree one less than the original polynomial since we are dividing by a first-degree polynomial.

If we perform the division correctly, the quotient that we obtain for T(x) / (x+9) should be x² - 2x - 8, which corresponds to option (c).