Question

p (x) is polynomial . Here are a few values of p(x). p(-5)=-2 p(-3) =6 p(3)=7 p(5)=-1 what is the remainder when p (x) is divided by (x+5)? what is the remainder when p(x) is divided by (x-3)?​

Answer 1

Answer:

When a polynomial p(x) is divided by (x-1), the remainder is 3. When p(x) is divided by (x-3), the remainder is 5. If r(x) is the remainder when p(x) is divided by (x -3) (x-1) then what will be the value of r(-2)?

Remainder theorem says that:

“When a polynomial p(x) is divided by (x−a) , the remainder is p(a) .”

Also, when a polynomial p(x) is divided by another polynomial q(x) ,the degree of the remainder is at most 1 less than the degree of q(x) .

Using the remainder theorem, we can write:

p(1)=3;p(3)=5

p(x) can be written as:

Dividend=(Divisor×Quotient)+Remainder

p(x)=(x−1)(x−3)Q(x)+r(x)

r(x) is the remainder polynomial and Q(x) is the Quotient polynomial. Since r(x) is linear, r(x)=Ax+B , where A and B are arbitrary constants.

⟹p(x)=(x−1)(x−3)Q(x)+Ax+B

Now,

p(1)=A+B=3⟹A+B=3

p(3)=3A+B=5⟹3A+B=5

Solving the 2 equations, we get A=1 and B=2 .

Therefore, r(x)=Ax+B=x+2

r(−2)=−2+2=0

Hence, r(−2)=0

Answer 2

Answer:

so for x+5 that is -2

and the other one is 7

Step-by-step explanation:

khan academy said it lol