(A) Let $p(x) = x^{3}-3x^{2}+ax+24$. Since $(x-2)$ is a factor of $p(x)$,by the Factor Theorem,$p(2) = 0$. Substituting $x = 2$ into the polynomial: $

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(A) Let $p(x) = x^{3}-3x^{2}+ax+24$. Since $(x-2)$ is a factor of $p(x)$,by the Factor Theorem,$p(2) = 0$. Substituting $x = 2$ into the polynomial: $p(2) = (2)^{3} - 3(2)^{2} + a(2) + 24 = 0$. $8 - 3(4) + 2a + 24 = 0$. $8 - 12 + 2a + 24 = 0$. $20 + 2a = 0$. $2a = -20$. $a = -10$.

Class 9 Mathematics Polynomials Mix Examples - Polynomials

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If $x-2$ is a factor of $x^{3}-3x^{2}+ax+24$,then $a = \ldots$

A
$-10$
B
$10$
C
$5$
D
$-5$

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If $x-2$ is a factor of $x^{3}-3x^{2}+ax+24$,then $a = \ldots$

Similar Questions

Classify the following as a constant,linear,quadratic,or cubic polynomial:$y^{3}-y$

Find the value of $m$ so that $2x - 1$ is a factor of $8x^4 + 4x^3 - 16x^2 + 10x + m$.

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

Evaluate the following using suitable identities: $(995)^{3}$

Write the following cube in expanded form:$(3x + 2y)^3$

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Classify the following as a constant,linear,quadratic,or cubic polynomial:
$y^{3}-y$

Write the following cube in expanded form:
$(3x + 2y)^3$