Find a and b for ax^3 - 8x^2 - 9x + b: Polynomial Remainder Theorem

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In this video, we solve the problem: Given that f(x) = ax^3 - 8x^2 - 9x + b is exactly divisible by 3x - 2, and leaves a remainder of 6 when divided by x, find the value of a and b.

This problem does not require you to find the quotient in order to determine the coefficients. You can simply use the Polynomial Remainder Theorem that for...

f(x) = p(x)q(x) + r;

r = f(a) for p = (x - a).

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Please ask me a maths question by commenting below and I will try to help you in future videos.

MasterWuMathematics
Master Wu
mathbff
PatrickJMT
Khan Academy
Mathematics

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NOTE: At 4:16, there is no need to multiply through the brackets in order to solve this problem. I've just included this as an extra step for completeness. You can simply evaluate f(2/3), rather than F(2/3).

MasterWuMathematics

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