Question

find the value of a if x+a is a factor of the polynomial x4-a2x2+3x-6a

Answer 1

If x+a is a factor of x4-a2x2+3x-a, then find the value of a?

By the factor theorem which states that if x - a is factor of a polynomial P(x) then P(a) = 0...so set that expression equal to 0 and substitute -a for all x's in the expression and solve for a...

P(-a) = (-a)^4 - a^2(-a)^2 + 3(-a) - a
0 = a^4 - a^(2+2) - 3a - a
0 = a^4 - a^4 - 3a - a <-- combine like terms..
0 = -4a <-- divide both sides of the equation by -4 to isolate 'a'...
0/-4 = -4a/-4
0 = a <-- answer....

So the value of 'a' is 0.

Answer 2

x+a is factor of x 4 −a 2 x 2 +3x−6a

Let p(x)=x 4 −a 2 x 2 +3x−6a

we know that if x−α is a factor of p(x) then

p(α)=0 So p(−a)=0

(−a) 4 −a 2 (−a) 2 +3(−a)−a=0

a 4 −a 4 −3a−a=0

−4a=0

a=0