Question

IV. If (x − 2) is factor of P(x) = x 2 + 2kx + 8 ,then find the value of k.

Answer 1

Answer:

here is your answer

Step-by-step explanation:

Answer:

value of k is -1

Step-by-step explanation:

If x-a is the factor of a polynomial f(x) then

\text{f(a)} = 0

We have to find the value of k:

if x-2 is a factor of p(x)=x^2+kx+2k.

then;

by definition we have;

p(2) = 2^2+2k+2k

4+4k = 0

Subtract 4 from both sides we have;

4k = -4

Divide both sides by 4 we get;

k = -1

Therefore, the value of k is -1

i hope it will be helpful

Answer 2

The answer is k = -3

Given: (x-2) is a factor of p(x) = x² + 2kx + 8  

To find: The value of k

Solution: (x-2) is a factor of p(x) = x² + 2kx + 8  

⇒ x-2 = 0 ⇒ x = 2

Note: (x-a) if factor of p(x) then p(a) must be equals to 0

To find k value substitute x = 2 in given equation p(x)

⇒ p(2) = 0

⇒ (2)² + 2k(2) + 8 = 0

⇒ 4 + 4k + 8 = 0

⇒ 4k + 12 = 0

⇒ 4k = -12

⇒ k = -12/4 = -3

Therefore, k value = -3

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