Question

If p(x) is exactly divisible by (x-a)f p(a) is equal to ​

Answer 1

If a polynomial (x) is divided by x-a, then what is the remainder?

Just rewrite your polynomial, x, featuring (x-a):

x=1×(x−a)+a

…so the quotient is clearly 1 and remainder is simply a.

EDIT in response to a comment: “what if the poster meant P(x), not (x), for the polynomial?” Good point (it did look like a suspiciously simple question…)

Then, if you divide a polynomial P(x) by (x-a) assume you will get a quotient Q(x) and a remainder r (with r being real number, as it can’t be an expression in x: it has to be of lower degree than (x-a), otherwise it would mean you’re not done dividing). You will have something like:

P(x)=Q(x)(x−a)+r⟹P(a)=Q(a)(a−a)+r=0+r=r

…so by calculating P(a), you find the remainder from the division of P(x) by (x-a)........

..... I hope it's helpful for u.....

#@misba9922

Answer 2

Answer:

The remainder will be p(a)

Here is the proof.

Let p(x) is divided by (x-a)

Then, by division algorithm of polynomials.

p(x) = (x-a) Q(x) + R

R is the remainder and it is a constant because according division algorithm degree of remainder is always less than degree of divisor and greater than Or equal to 0. So it is 0.

Q(x) is quotient.

Now, if we particularly put x = a in the equation, we get.

p(a) = ( a-a) Q(a) + R

p(a) = R

which is our required remainder.

Hence, p(a) is the remainder.