Question

find the value of a if x + 2is factor of 4x⁴ + 2x³- 3x² + 8x + 5a

please solve ​

Answer 1

Answer:

Given X+2 is a factor of 4X⁴+2X³-3X²+8X+5a,

the remainder must be zero.

The zero of X+2 is -2,

Let f(X) be the given polynomial

Substituting X=-2

f(-2)=4(-2)⁴+2(-2)³-3(-2)²+8(-2)+5a

f(-2)=64+2(-8)-3(4)-16+5a

0=64-16-12-16+5a

0=20+5a

5a=-20

thus a =-20/5=-4

Answer 2

if x + 2 is factor then x+2=0

x= -2

substitute x = -2

in the big equation

4(-2)^4 +2(-2)^3-3(-2)^2 +8(-2) +5a =0

after caluculation

64 - 16 -12 - 16 + 5a =0

64 - 32 - 12 + 5a =0

64 - 44 + 5a =0

20 + 5a =0

5a= -20

a = -4

(please spare me if their are any mistakes)