Question

What must be added to the polynomial x power 4 + 2 x cube minus 2 x square + x - 1 so that the resulting polynomial is exactly divisible by x square + 2 x minus 3?

Answer 1

Answer:

x-2

For finding the number to be added with f(x) we will divide f(x) with g(x) and the remainder will be the number to be added.

Answer 2

Given : p(x) = $x^4 +2x^3-2x^2+x-1$

divisor = x²+2x-3

Explanation:

p(x) = $x^4 +2x^3-2x^2+x-1$

divisor = x²+2x-3

now , on dividing p(x) by g(x)

we get

Quotient = x²+1

Remainder = -x+2

thus ,

we should add - (-x+2) to make it divisible by x²+2x-3

Thus , we should add x-2 to the p(x)

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