Question

If 2x+k is a factor of the polynomial 8x^3+4kx^2+3x+k-1, then find the value of k

Answer 1

this is the best solution of the ques hope u understood ans is k=2 I take polynomial as f okk best of luck

Answer 2

Given,

If 2x+k is a factor of the polynomial 8x³+4kx²+3x+k-1.

To find,

The value of k

Solution,

2x+k=0

2x=-k

x=-k/2

Since  2x+k is a factor of the polynomial  8x³+4kx²+3x+k-1 so it would satisfy the polynomial.

⇒  8x³+4kx²+3x+k-1 = 0

⇒  8(-k/2)³+4k(-k/2)²+3(-k/2)+k-1=0

⇒  -(8k³/8) + 4k(k²/4)+-3k/2 + k-1=0

⇒  -k³+k³+3k/2+k-1=0

⇒  (k/2)-1=0

⇒  k/2=1

⇒  k=2.

Hence, if 2x+k is a factor of the polynomial  8x³+4kx²+3x+k-1 , then the value of k would be 2.