# When P(x) = x^3 + 2x + a is divided by x - 2, the remainder is 4, how do you find the value of a?

##### 1 Answer
Jul 28, 2015

Using the Remainder theorem.

$a = - 8$

#### Explanation:

According to the Remainder theorem, if $P \left(x\right)$ is divided by $\left(x - c\right)$ and the remainder is $r$ then the following result is true :

$P \left(c\right) = r$

In our problem,

$P \left(x\right) = {x}^{3} + 2 x + a \text{ }$ and

To find the value of $x$ we have to equate the divisor to zero : $x - 2 = 0 \implies x = 2$

The remainder is $4$

Hence $P \left(2\right) = 4$

$\implies {\left(2\right)}^{3} + 2 \left(2\right) + a = 4$

$\implies 8 + \textcolor{\mathmr{and} a n \ge}{\cancel{\textcolor{b l a c k}{4}}} + a = \textcolor{\mathmr{and} a n \ge}{\cancel{\textcolor{b l a c k}{4}}}$

$\implies \textcolor{b l u e}{a = - 8}$