Question

Find the remainder when f(x) = x Power 4 - 3x square + 4 is divided by g (x) = x-2 and verify the result by actual division.

Answer 1

Given Equations :

• f(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

$\boxed{ \sf{x = 2}}$

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.

$\sf{Hence \: Verified!}$

Answer 2

Answer:

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Step-by-step explanation:

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