# When the expression 2x^3 + ax^2 -5x -2 is divided by 2x-1, the remainder is -3.5 . Determine the value of the constant a. Can someone please help?

## When the expression $2 {x}^{3} + a {x}^{2} - 5 x - 2$ is divided by $2 x - 1$, the remainder is $- 3.5$ . Determine the value of the constant $a$.

May 21, 2018

$a = 3$

#### Explanation:

The remainder theorem states that if $P \left(x\right)$ is divided by $x - a$, then the remainder is given by $P \left(a\right)$.

Therefore:

$2 {\left(\frac{1}{2}\right)}^{3} + a {\left(\frac{1}{2}\right)}^{2} - 5 \left(\frac{1}{2}\right) - 2 = - 3.5$

A little bit of algebra lets us simplify to

$2 \left(\frac{1}{8}\right) + a \left(\frac{1}{4}\right) - \frac{5}{2} = - 1.5$

$\frac{1}{4} a = - \frac{3}{2} + \frac{5}{2} - \frac{1}{4}$

$4 \left(\frac{1}{4} a\right) = 4 \left(- \frac{3}{2} + \frac{5}{2} - \frac{1}{4}\right)$

$a = - 6 + 10 - 1$

$a = 3$

Hopefully this helps1