Question

If (x-8) is a product of (x³-11x²+14x+80). What are the two remaining products?

A) x²+3x−10 and x+8
B) x²-3x−10 and x−8
C) x²+3x+10 and x−8
D) x²−3x+10 and x+8

Answer 1

To find the two remaining products, we need to factorize the equation. The two remaining products are x²+3x+10 and x-8.

Step-by-step explanation:

The given equation is (x-8) = (x³-11x²+14x+80). The student's question is asking to find the remaining factors of a cubic polynomial given that (x-8) is one of the factors. The polynomial is (x³-11x²+14x+80). To find the other factors, we perform polynomial long division or use synthetic division with the known factor (x-8). To find the two remaining products, we need to factorize the equation. Let's start by using synthetic division to divide x³-11x²+14x+80 by (x-8). We get a quotient of x²+3x+10 and a remainder of 0. So, the two remaining products are x²+3x+10 and x-8.