Question

find the remainder when f(x)=x⁴-3x²+4 is divied by g (x) =x-2 and verify the result by actual division​

Answer 1

Answer:

Step-by-step explanation: Given : f(x)=x  

4

−3x  

2

+4

f(2)=(2)  

4

−3(2)  

2

+4

=16−12+4=8

Answer 2

Step-by-step explanation:

Given :-

f(x)=x⁴-3x²+4

g (x) =x-2

To find :-

Find the remainder when f(x)=x⁴-3x²+4 is divied by g (x) =x-2 and verify the result by actual division ?

Solution :-

Given polynomial is f(x)=x⁴-3x²+4

Given divisor is g (x) =x-2

We know that

By, Remainder Theorem

If f(x) is divided by g(x)=x-2 then the remainder is f(2).

=> f(2) = 2⁴-3(2)²+4

=> f(2) = 16-3(4)+4

=> f(2) = 16-12+4

=> f(2) = 20-12

=> f(2) = 8

The , remainder = 8

Check :-

f(x) ÷ g(x)

x-2 ) x⁴+0x³-3x²+0x+4 ( x³+2x²+x+2

x⁴-2x³

(-) (+)

___________

2x³-3x²

2x³-4x²

(-) (+)

____________

x²+0x

x²-2x

(-) (+)

_____________

2x+4

2x-4

(-) (+)

______________

8

______________

Remainder = 8

Verified.

Used Theorem :-

Remainder Theorem:-

Let P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if P (x) is divided by x-a then the remainder is P(a).

Used Method:-

→ Long Division