What should be subtracted from p(x) = x^{2} + | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the polynomial be $p(x) = x^{2} + 9x + 20$. According to the Remainder Theorem,if $p(x)$ is divided by $(x + 2)$,the remainder is $p(-2)$. Sub

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) Let the polynomial be $p(x) = x^{2} + 9x + 20$. According to the Remainder Theorem,if $p(x)$ is divided by $(x + 2)$,the remainder is $p(-2)$. Substitute $x = -2$ into the polynomial: $p(-2) = (-2)^{2} + 9(-2) + 20$ $p(-2) = 4 - 18 + 20$ $p(-2) = 6$. For the polynomial to be divisible by $(x + 2)$,the remainder must be $0$. Therefore,we must subtract the remainder $6$ from the polynomial $p(x)$ so that the new polynomial becomes divisible by $(x + 2)$.

What should be subtracted from $p(x) = x^{2} + 9x + 20$ so that the resulting polynomial is divisible by $x + 2$?

Similar Questions

One of the factors of $(25 x^{2}-1)+(1+5 x)^{2}$ is

Zero of the polynomial $p(x) = 2x + 5$ is

Find the quotient and the remainder when $x^{3}+x^{2}-10x+8$ is divided by $x+3$.

On dividing $p(x) = 2x^3 - 3x^2 + ax - 3a + 9$ by $(x + 1)$,if the remainder is $16$,then find the value of $a$. Then,find the remainder on dividing $p(x)$ by $(x + 2)$.

The polynomial $p(x) = x^{4} - 2x^{3} + 3x^{2} - ax + 3a - 7$ when divided by $x + 1$ leaves the remainder $19$. Find the value of $a$. Also,find the remainder when $p(x)$ is divided by $x + 2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module