Answer:
141
Step-by-step explanation:
The given polynomial to us is ,
[tex]\implies f(x) = 4x^5 + 3x^2 + 1 [/tex]
And we need to find out the remainder when it is divided by ,
[tex]\implies g(x) = x - 2 [/tex]
Using the Remainder Theorem , firstly equate [tex] g(x) [/tex] with zero . So that ,
[tex]\implies x - 2 = 0 [/tex]
Add 2 on both sides ,
[tex]\implies x = 2 [/tex]
Therefore here the remainder will be [tex]f(2)[/tex].Now substitute x = 2 in f(x) .
[tex]\implies f(2) = 4(2)^5 + 3(2)^2 + 1 [/tex]
Simplify the exponents ,
[tex]\implies f(2) = 4 (32) + 3(4) + 1[/tex]
Solve the brackets ,
[tex]\implies f(2) = 128 + 12 +1 [/tex]
Add the terms ,
[tex]\implies \boxed{\quad f(2) = 141 \quad} [/tex]
Hence the remainder is 141 when f(x) is divided by (x-2) .
