Factorization of polynomials

Algebra Level 2

If ax^3+bx^2+x-6 has x+2 as a factor and leaves remainder 4 when divided by (x-2), find the values of a and b.

a=0 b=2 a=4 b=5 a=0 b=3 a=2 b=0

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1 solution

John Doe
Jul 28, 2015

By Polynomial remainder theorem:

8 a + 4 b 8 = 0 {-8}{a}\mathrm{{+}}{4}{b}\mathrm{{-}}{8}\mathrm{{=}}{0}

8 a + 4 b 4 = 4 {8}{a}\mathrm{{+}}{4}{b}\mathrm{{-}}{4}\mathrm{{=}}{4}

where a=0 and b=2

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