(A) Let $p(x) = x^{3} + 13x^{2} + ax + 35$.Since $x+5$ is a factor of $p(x)$,by the Factor Theorem,$p(-5) = 0$.Substituting $x = -5$ into the polynomi

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(A) Let $p(x) = x^{3} + 13x^{2} + ax + 35$.Since $x+5$ is a factor of $p(x)$,by the Factor Theorem,$p(-5) = 0$.Substituting $x = -5$ into the polynomial:$(-5)^{3} + 13(-5)^{2} + a(-5) + 35 = 0$$-125 + 13(25) - 5a + 35 = 0$$-125 + 325 - 5a + 35 = 0$$235 - 5a = 0$$5a = 235$$a = 47$.

Class 9 Mathematics Polynomials Mix Examples - Polynomials

Medium

If $x+5$ is a factor of $x^{3}+13x^{2}+ax+35$,find the value of $a$.

A
$a = 47$
B
$a = 45$
C
$a = 49$
D
$a = 51$

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If $x+5$ is a factor of $x^{3}+13x^{2}+ax+35$,find the value of $a$.

Similar Questions

Factorise the following quadratic polynomial by splitting the middle term:$15x^2 + 7x - 2$

Without finding the cubes,factorise $(x-y)^{3}+(y-z)^{3}+(z-x)^{3}$.

Expand the following:$(4a - b + 2c)^2$

Check whether $p(x)$ is a multiple of $g(x)$ or not,where $p(x) = x^{3} - x + 1$ and $g(x) = 2 - 3x$.

Which of the following is one of the zeros of the polynomial $x^{3}-3x^{2}-5x+15$?

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Factorise the following quadratic polynomial by splitting the middle term:
$15x^2 + 7x - 2$

Expand the following:
$(4a - b + 2c)^2$