Question

If f(x) = 4x5 + 3x2 + 1, then what is the remainder when f(x) is divided
by X – 2?

Answer 1

141

Explanation:

The given polynomial to us is ,

`\implies f(x) = 4x^5 + 3x^2 + 1`

And we need to find out the remainder when it is divided by ,

`\implies g(x) = x - 2`

Using the Remainder Theorem , firstly equate
`g(x)` with zero . So that ,

`\implies x - 2 = 0`

Add 2 on both sides ,

`\implies x = 2`

Therefore here the remainder will be
`f(2)`.Now substitute x = 2 in f(x) .

`\implies f(2) = 4(2)^5 + 3(2)^2 + 1`

Simplify the exponents ,

`\implies f(2) = 4 (32) + 3(4) + 1`

Solve the brackets ,

`\implies f(2) = 128 + 12 +1`

Add the terms ,

`\implies \boxed{\quad f(2) = 141 \quad}`

Hence the remainder is 141 when f(x) is divided by (x-2) .