(B) Let $p(x) = x^{3} + ax^{2} + 19x + 20$. According to the Remainder Theorem,when $p(x)$ is divided by $(x + 3)$,the remainder is $p(-3)$. Given tha

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(B) Let $p(x) = x^{3} + ax^{2} + 19x + 20$. According to the Remainder Theorem,when $p(x)$ is divided by $(x + 3)$,the remainder is $p(-3)$. Given that the remainder is $a$,we have $p(-3) = a$. Substituting $x = -3$ into the polynomial: $(-3)^{3} + a(-3)^{2} + 19(-3) + 20 = a$ $-27 + 9a - 57 + 20 = a$ $9a - 64 = a$ $8a = 64$ $a = 8$.

Class 9 Mathematics Polynomials Mix Examples - Polynomials

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On dividing $x^{3} + ax^{2} + 19x + 20$ by $(x + 3)$,if the remainder is $a$,then find the value of $a$.

A
$7$
B
$8$
C
$9$
D
$10$

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Class 9

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Polynomials

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Mix Examples - Polynomials

Find $p(1)$,$p(2)$,and $p(4)$ for the following polynomial:
$p(x) = x^{2} - 3x + 2$

Easy

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If the polynomials $az^{3}+4z^{2}+3z-4$ and $z^{3}-4z+a$ leave the same remainder when divided by $z-3$,find the value of $a$.

Medium

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Degree of the polynomial $4 x^{4}+0 x^{3}+0 x^{5}+5 x+7$ is

Easy

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Which of the following is a factor of $(x+y)^{3}-(x^{3}+y^{3})$?

Easy

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Classify the following polynomial as a polynomial in one variable,two variables,etc.
$y^{3}-5y$

Easy

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On dividing $x^{3} + ax^{2} + 19x + 20$ by $(x + 3)$,if the remainder is $a$,then find the value of $a$.

Similar Questions

Find $p(1)$,$p(2)$,and $p(4)$ for the following polynomial:$p(x) = x^{2} - 3x + 2$

If the polynomials $az^{3}+4z^{2}+3z-4$ and $z^{3}-4z+a$ leave the same remainder when divided by $z-3$,find the value of $a$.

Degree of the polynomial $4 x^{4}+0 x^{3}+0 x^{5}+5 x+7$ is

Which of the following is a factor of $(x+y)^{3}-(x^{3}+y^{3})$?

Classify the following polynomial as a polynomial in one variable,two variables,etc.$y^{3}-5y$

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Find $p(1)$,$p(2)$,and $p(4)$ for the following polynomial:
$p(x) = x^{2} - 3x + 2$

Classify the following polynomial as a polynomial in one variable,two variables,etc.
$y^{3}-5y$