Question

what must be subtracted from polynomial p(x) =x⁴-5x+6 such that the resulting polynomial is exactly divisible by 2-x²​

Answer 1

Answer:

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Step-by-step explanation:

According to the question, we have f(x)=x

4

+2x

3

−13x

2

−12x+21 and g(x)=x

2

−4x+3

We know : Dividend = Quotient X Divisor + Remainder

Hence f(x)=q(x)×g(x)+r(x)

g(x)=

q(x)

f(x)−r(x)

So , r(x) must be subtracted so that result is exactly divisible by x

2

−4x+3

Ans : 2x - 3