• Dec 30th 2008, 01:46 AM
greghunter
When 2x^3 + ax^2 + x + 1 is divided by x + 2 the remainder is -29. Find a.
• Dec 30th 2008, 01:51 AM
Mathstud28
Quote:

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

When we divide this (is that what you are having trouble with?) we get the remainder to be $\displaystyle \frac{4a-17}{x+2}$. So solving $\displaystyle 4a-17=-29$ gives $\displaystyle a=-3$
• Dec 30th 2008, 01:56 AM
Pn0yS0ld13r
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 AM
mr fantastic
Quote:

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

When the polynomial $\displaystyle p(x)$ is divided by $\displaystyle \alpha x - \beta$ the remainder is $\displaystyle p\left( \frac{\beta}{\alpha}\right)$.

Therefore $\displaystyle p(-2) = 2(-2)^3 + a(-2)^2 + (-2) + 1 = -29$. Solve for $\displaystyle a$.