Question

Find the remainder when p(x) = x4 - 27 is divided by x - 4.

Answer 1

Answer:

229 is the remainder.

Explanation:

In order to find the remainder, insert the value of x in the equation.

Given equation:

• $\sf p(x) = x^4 - 27$

Given x value:

• x - 4 = 0

• x = 4

Find remainder:

$\sf p(4) = 4^4 - 27$

$\sf p(4) = 256 - 27$

$\sf p(4) = 229$

Answer 2

Answer:

229

Step-by-step explanation:

Here we are given a polynomial p(x) and we need to find the remainder when it is divided by (x-4) . As we know that if a polynomial, say $g(x)$ is divided by $x-a$ then the remainder is $g(a)$ .

Firstly equate $x -4$ with 0 , we have;

$\longrightarrow x -4=0$

$\longrightarrow x =0+4$

$\longrightarrow x = 4$

Now substitute $x =4$ in $p(x)$ ,

$\longrightarrow p(x)= x^4-27$

$\longrightarrow p(4)= (4)^4-27$

$\longrightarrow p(4) = 256 - 27$

$\longrightarrow \underline{\underline{\boldsymbol{ p(4) = 229}}}$

Hence the remainder is 229 .