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

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Answer 1 · 2015-07-28T10:31:50

Using the Remainder theorem.

$a=-8$

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

$P(c)=r$

In our problem,

$P(x)=x^3+2x+a" "$ and

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

The remainder is $4$

Hence $P(2)=4$

$=>(2)^3+2(2)+a=4$

$=>8+color(orange)cancel(color(black)4)+a=color(orange)cancel(color(black)4)$

$=>color(blue)(a=-8)$

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