Question

Find the value of a if x + a is a factor of x4-a2x2 +3x-a?​

Answer 1

Answer:

p(x) = x⁴-a²x²+3x-a

x+a is a factor,

Hence x=-a

p(-a)=(-a)⁴-a²(-a)²+3(-a)-a

=a⁴-a⁴-3a-a

= -4a

Answer 2

Answer:

$p(x) = {x}^{4} - {a}^{2} {x}^{2} + 3x - a$

If x+a is a factor of the polynomial,

$x + a = 0$

$x = - a$

Replacing x to -a in the given equation, we get:

$p( - a) = {( - a)}^{4} - {a}^{2} {( - a)}^{2} + 3( - a) - a$

$p( - a) = {a}^{4} - {a}^{4} - 3a - a$

$0 = - 4a$

$4a = 0$

$a = 0$

Hope this helps.

Thanks.