Question

if p(x)=(x-a)q(x) then find the degree of q(x)

Answer 1

Step-by-step explanation:

p(x)=(x-a)q(x)+r(x)

where q(x) is the quotient when f(x) is divided by x-a and r(x) 

The Remainder Theorem says that we can restate the polynomial in terms of the divisor, and then evaluate the polynomial 

x=a

hence putting it we get

p(a)=0*q(a)+r(a)

p(a)=r(a)

hence  the remainder is p(a)

Answer 2

The degree of q(x) is p(x)-1

Given:

p(x)=(x-a)q(x)

To find:

The degree of q(x)

Solution:

Here, the idea of a polynomial degree will be applied. comparing the x degree on both

In this case, (x-a) is increased by q(x). Consequently, the degree of the total product that equals p(x) will be as follows:

⇒p(x) = q(x) + 1

Therefore, q(x) = p(x) - 1

Hence, the degree of p(x) - 1 is equal to the degree of q(x).

Therefore, the degree of q(x) is p(x)-1.

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