7. Find the remainder when f(x) = x^4 - 3x² +4 is divided by g(x)= x - 2 and verify the
result by actual division.
Answers
Answer:
please mark my answer as brainliest and please follow me
Explanation:
GIVEN :
Find the remainder when f(x)=x^4-3x^2+4f(x)=x
4
−3x
2
+4 is divided by g(x)=x-2 and verify the result by actual division
TO FIND :
The remainder when f(x)=x^4-3x^2+4f(x)=x
4
−3x
2
+4 is divided by g(x)=x-2 and verify the result by actual division
SOLUTION :
Given that the functions are f(x)=x^4-3x^2+4f(x)=x
4
−3x
2
+4 is divided by g(x)=x-2 and verify the result by actual division
Put x=2 in f(x) we get
f(2)=2^4-3(2)^2+4f(2)=2
4
−3(2)
2
+4
=16-12+4
=20-12
=8
⇒ f(2)=8
∴ remainder = 8
Now we can verify it by actual division method, f(x) can be written as f(x)=x^4+0x^3-3x^2+0x+4f(x)=x
4
+0x
3
−3x
2
+0x+4
Now divide f(x) by g(x) as below :
x^3+2x^2+x+2x
3
+2x
2
+x+2
_____________________
x-2 ) x^4+0x^3-3x^2+0x+4x
4
+0x
3
−3x
2
+0x+4
x^4-2x^3x
4
−2x
3
_(-)__(+)____
2x^3-3x^22x
3
−3x
2
2x^3-4x^22x
3
−4x
2
_(-)___(+)______
x^2+0xx
2
+0x
x^2-2xx
2
−2x
__(-)__(+)______
2x+4
2x-4
_(-)_(+)___
8
________
When the given function f(x) is divided by g(x) then the remainder is 8 and it is verified by actual division.
∴ remainder = 8