Question

if X + 2 factor of x power 4 the square minus 4 then what will the value of what will the value of a​

Answer 1

Answer:

Consider the given polynomial is

P(x)=4x^4+2x^3-3x^2+8x+5aP(x)=4x

4

+2x

3

−3x

2

+8x+5a

We need to find the value of a when (x+2) is a factor of P(x).

If (x-c) is a factor of P(x), the P(c)=0.

Since (x+2) is a factor of P(x), it means P(-2)=0.

Substitute x=-2 in the given polynomial.

P(-2)=4(-2)^4+2(-2)^3-3(-2)^2+8(-2)+5aP(−2)=4(−2)

4

+2(−2)

3

−3(−2)

2

+8(−2)+5a

P(-2)=4(16)+2(-8)-3(4)-16+5aP(−2)=4(16)+2(−8)−3(4)−16+5a

P(-2)=20+5aP(−2)=20+5a

Equate P(-2)=0.

20+5a=020+5a=0

5a=-205a=−20

Divide both sides by 5.

a=-4a=−4