Question

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

Answer 1

Answer:

141

Step-by-step 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) .