# For what value of a is (x – 5) a factor of

Question:

For what value of $a$ is $(x-5)$ a factor of $x^{3}-3 x^{2}+a x-10$

Solution:

Here, $f(x)=x^{3}-3 x^{2}+a x-10$

By factor theorem

If (x - 5) is the factor of f(x) then, f(5) = 0

⟹ x - 5 = 0

⟹ x = 5

Substitute the value of x in f(x)

$f(5)=5^{3}-3(5)^{2}+a(5)-10$

= 125 - (3 * 25) + 5a - 10

= 125 - 75 + 5a - 10

= 5a + 40

Equate f(5) to zero

f(5) = 0

⟹ 5a + 40 = 0

⟹ 5a = - 40

⟹ a = − 40/5

= - 8

When a = - 8, (x - 5) will be factor of f(x)