Question

Find the value of k, if x+2 is a factor of $4x^{4} + 2^{3} - 3x^{2}$ +8x + 5k
Please give in explantion form

Answer 1

Step-by-step explanation:

Let f(x) = 4x4 + 2x3 - 3x2 + 8x + 5a be the given polynomial From factor theorem

if (x+2) factor of f(x) then f(-2) = 0 Now,

f(x)= 4xr* + 2x – 3x² +8x+5a %3D

=f(-2)

=0

= 4(-2)* +2(-2) –3(-2)° +8(-2)+5a

= 0

= 64-16-12–16+5a

= 0

=5a+ 20

= 0

= 5a

= 20 >la

=- Hence (x+2) is a factor of f (x)when a =-4