When 2x^2+(4-p)x-2p=0,x=-2 is a solution. Which is a factor of 2x^2+(4-p)x-2p a) 2x-p b)2x+p c)4-p d)x-2p Please show work. Thank you :)?

x = -2 is a solution of the equation 2x² + (4 - p)x - 2p = 0
Then, (x + 2) is a factor of 2x² + (4 - p)x - 2p.

Let (ax + b) be another factor of 2x² + (4 - p)x - 2p.

(x + 2)(ax + b) = 2x² + (4 - p)x - 2p
ax² + bx + 2ax + 2b = 2x² + (4 - p)x - 2p
ax² + (b + 2a)x + 2b = 2x² + (4 - p)x - 2p

Compare the coefficient of x²: a = 2
Compare the constant term: 2b = -2p, i.e. b = -p

Hence ax + b = 2x - p is a factor of 2x² + (4 - p)x - 2p.

..... The answer is: a) 2x - p

(x + 2) is a factor of the quadratic.
You can try and expand each possible factor with (x - 2). The correct answer is A).
∴ (x + 2)(2x - p) = 2x^2 - px + 4x - 2p
= 2x^2 + (4 - p)x - 2p
Therefore, (2x - p) is a factor.

Hope this helps !!!!!!!