Q. 35.0( 1 Vote )

# Find the value of k if (x – 5) is a factor of the polynomial x^{3} – 3x^{2} + kx – 10.

Answer :

Using Remainder Theorem:

Putting factor = 0, we get -

(x – 5) = 0

⇒ x = 5.

Now, ∵ it is given that (x – 5) is a factor of the polynomial x^{3} –

3x^{2} + kx – 10.

⇒ If we substitute x = 5 in x^{3} – 3x^{2} + kx – 10, the remainder will be zero.

⇒ 5^{3} – 3(5)^{2} + k(5) – 10 = 0

⇒ 125 – 3× 25 + 5k – 10 = 0

⇒ 125 – 75 + 5k – 10 = 0

⇒ 5k + 40 = 0

⇒ k = – 8

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