Question

X-2 divided by actual division x to the power 4 - 3 square +4

Answer 1

Answer:

I hope this answer will help you if(x) = x⁴ + 0x³- 3x² + 0x + 4 and g(x) = x - 2

By remainder theorem, we can make g(x) = 0 and find the value of x.

⟹ x - 2 = 0

\boxed{ \sf{x = 2}}

x=2

Substituting the value of x in f(x),

⟹ f(x) = x⁴ + 0x³ - 3x² + 0x + 4

⟹ f(2) = (2)⁴ + 0(2)³ - 3(2)² + 0(2) + 4

⟹ f(2) = 16 + 0 - 12 + 0 + 4

⟹ f(2) = 8

So by using remainder theorem, we got the remainder as 8.

___________________

Let us now verify the result by using actual long division method.

Have a look at the attachment!

After dividing f(x) by g(x), we got :

The Quotient as x³ + 2x² + x + 2

The remainder as 8.

\sf{Hence \: Verified!}HenceVerified!