Thread: Remainder Theorem

Hey guys, check this question out - its a toughie for sure :

The expression f(x) = ax^3+bx^2-10x+24 is exactly divisible by x^2-2x-8. Find a and b. Solve f(x) = 0. Find the remainder when f(x) is divided by x-2.

Originally Posted by Himerzi

Hey guys, check this question out - its a toughie for sure :

The expression f(x) = ax^3+bx^2-10x+24 is exactly divisible by x^2-2x-8. Find a and b. Solve f(x) = 0.

use long division of polynomials to divide f(x) by x^2 - 2x - 8. note that the remainder must be zero. you will be able to solve for a and b

note that f(x) = q(x) * (x^2 - 2x - 8) = q(x) * (x - 4)(x + 2)

obviously x = 4 and x = -2 are two zeros. the last zero comes from the zero of q(x). q(x) is the quotient you get from the division you did before.

Find the remainder when f(x) is divided by x-2.

this is f(2)