Question

What is the remainder when x^2 + 5x - 24 is divided by x - 6?

Answer 1

Given:

The dividend is,

`x^2+5x-24`

The divisor is,

`x-6`

To find: The remainder

Step-by-step explanation:

Let us take,

`p(x)=x^2+5x-24`

Using the remainder theorem,

Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number.

If p(x) is divided by the linear polynomial x - a, then the remainder is p(a).

Here,

`a=6`

Substitute the value of a in the above polynomial.

`\begin{gathered} p(6)=6^2+5(6)-24_{} \\ =36+30-24 \\ =42 \end{gathered}`

Hence, the remainder is 42.

Final answer: The remainder is 42.