Question

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

Answer 1

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 .

Answer 2

229 is the remainder.

Step-by-step 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`