Question

p(x)= x³ – 4 and q(x)= x+2 then degree of p(x)×q(x) is​

Answer 1

p(x) =x3 Answer

Step-by-step explanation:

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Answer 2

Answer:

As P(x) is the sum of GP. = 1−x1−x6

It has 5 roots , let a1,a2,a3,a4,a5, and they are the 6th roots of unity except  unity.

NowP(x12)=1+x12+x24+x36+x48+x60=P(x).Q(x)+R(x).

Here R(x) is a remainder and a polynomial of maximum degree 4.

Put x=a1,a2...............,a5

We get,

R(a1)=6, R(a2)=6 ,R(a3)=6, R(a4)=6, R(a5)=6

i.e, R(x)−6=0 has 6 roots.

Which contradict that R(x) is maximum of degree 4.

So, it is an identity

Therefore, R(x)=6.

Step-by-step explanation:

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