Question

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HERE'S MY QUESTION

Answer 1

Hey buddy!
Here's the answer to the 14th question!
Hope it helps you!

Answer 2

Hi friend!!

Given, x⁴-2x³+3x²-ax+b

when the given polynomial is divided by x-1, the simple way to find the remainder is by substituting x=1 (because for x=1, x-1 will be 0)

→ (1)⁴-2(1)³+3(1)²-a(1)+b=5 (given)

1-2+3-a+b=5

2-a+b=5

a-b+3=0------(1)

When it is divided by x+1 , the remainder will be calculated by substituting x=-1(bcoz for x=-1, x+1 will be 0)

(-1)⁴-2(-1)³+3(-1)²-a(-1)+b=19

1+2+3+a+b=19

a+b-13=0-----(2)

By solving (1) and (2) , we get a=5,b=8

Now, the polynomial becomes

x⁴-2x³+3x²-ax+b =x⁴-2x³+3x²-5x+8

so, Now when the polynomial is divided by x-2, the remainder will be simply calculated by substituting x=2

→remainder=(2)⁴-2(2)³+3(2)²-5(2)+8

=16-16+12-10+8

=10.

I hope this will help u ;)