How do I factor this problem out?

Question

Answer 1

Favorite Answer

Use the remainder theorem

f(x) = x^4+x^2-6

a)f(-3) = 81+9-6 = 84

∴ (x+3) is not a factor

b) f(√2) = 4+2-6 = 0

∴ (x-√2) is a factor

Answer 2

Let x^2 = a. Then what you got is a^2 + a - 6. This in turn becomes (a - 2)(a + 3) when factoring. Now resubstitute x^2, and the full factoring is (x^2 - 2)(x^2 + 3).

Is x + 3 a factor of P(x)? No. For that to be true, x = -3 must result in P(x) = 0, but if x = -3, ((-3)^2 - 2)((-3)^2 + 3) = 7 * 12 = 84. Not 0, so x + 3 is not a factor.

Is x - sqrt(2) a factor of P(x)? Yes. See that factor x^2 - 2? You CAN factor that as a difference of squares: x^2 - 2 = (x + sqrt(2))(x - sqrt(2)). There's your x - sqrt(2).

Answer 3

snuggle right up to some boobies, and use the brain and think for it, if not review the last 3 pages of the homework for the problem.