Question

find the value of K for which(x-1) is a factor of (2xpower3+9xpower2+x+​

Answer 1

Question:

Find the value of K for which (x-1) is a factor of 2x³ + 9x² + x + k.

Answer:

The value of k is - 12.

Step-by-step-explanation:

The given polynomial is 2x³ + 9x² + x + k.

Let the polynomial be P ( x ).

We have given that,

( x - 1 ) is a factor of the given polynomial.

By factor theorem,

If x = 1, P ( x ) = 0

∴ 2 * ( 1 )³ + 9 * ( 1 )² + 1 + k = 0

⇒ 2 * 1 + 9 * 1 + 1 + k = 0

⇒ 2 + 9 + 1 + k = 0

⇒ 2 + 10 + k = 0

⇒ 12 + k = 0

⇒ k = - 12

∴ The value of k is - 12.