When 2x^3 + ax^2 + x + 1 is divided by x + 2 the remainder is -29. Find a.
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
$\displaystyle f(-2)=2(-2)^{3} + a(-2)^{2}+(-2)+1=4a-17=-29$
$\displaystyle 4a-17=-29$
$\displaystyle a=-3$.