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.

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- Sep 28th 2008, 07:21 PMHimerziRemainder 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. - Sep 28th 2008, 07:51 PMJhevon
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.

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