Question

determine the remainder when the function p(x)=12x^3-10x^2-5x+18 is divided by 2x-5. express answer in decimal form

Answer 1

The remainder is 130.5

EXPLANATION :

Note that the remainder when P(x) is divided by (x - a) can be obtain at P(a).

From the given problem,

`P(x)=12x^3-10x^2-5x+18`

2x - 5,

Solve first the value of x by equating the divisor to 0.

2x - 5 = 0

2x = 5

x = 5/2 = 2.5

Substitute x = 2.5 to the function.

`\begin{gathered} P(2.5)=12(2.5)^3-10(2.5)^2-5(2.5)+18 \\ P(2.5)=187.5-62.5-12.5+18 \\ P(2.5)=130.5 \end{gathered}`