Question

if p(x) is divided by x-a, then the remainder is_

​

Answer 1

Answer:

p(a) by remainder theorem please mark brainliest

Answer 2

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

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.

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).

2.7 million jobs estimated for data science roles in 2020.

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.