When 2x^3 + ax^2 + x + 1 is divided by x + 2 the remainder is -29. Find a.

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- Dec 30th 2008, 01:46 AMgreghunterplease help! remainder theorems and long division
When 2x^3 + ax^2 + x + 1 is divided by x + 2 the remainder is -29. Find a.

- Dec 30th 2008, 01:51 AMMathstud28
- Dec 30th 2008, 01:56 AMPn0yS0ld13r
Use the remainder theorem, Polynomial remainder theorem - Wikipedia, the free encyclopedia

Let $\displaystyle f(x) = 2x^{3} + ax^{2} + x + 1$.

When f(x) is divided by x + 2 the remainder is -29. Thus the remainder theorem says that $\displaystyle f(-2) = -29$.

Hence

$\displaystyle f(-2)=2(-2)^{3} + a(-2)^{2}+(-2)+1=4a-17=-29$

$\displaystyle 4a-17=-29$

$\displaystyle a=-3$. - Dec 30th 2008, 01:57 AMmr fantastic