Answer:
(3 x^2 + 1) (x^2 - 2)
Step-by-step explanation:
Factor the following:
3 x^4 - 5 x^2 - 2
Hint: | Express 3 x^4 - 5 x^2 - 2 as a quadratic in x^2.
3 x^4 - 5 x^2 - 2 = 3 (x^2)^2 - 5 x^2 - 2:
3 (x^2)^2 - 5 x^2 - 2
Hint: | Factor 3 (x^2)^2 - 5 x^2 - 2 which is quadratic with respect to x^2.
Factor the quadratic 3 (x^2)^2 - 5 x^2 - 2. The coefficient of x^4 is 3 and the constant term is -2. The product of 3 and -2 is -6. The factors of -6 which sum to -5 are 1 and -6. So 3 (x^2)^2 - 5 x^2 - 2 = 3 x^4 - 6 x^2 + x^2 - 2 = x^2 (3 x^2 + 1) - 2 (3 x^2 + 1):
x^2 (3 x^2 + 1) - 2 (3 x^2 + 1)
Hint: | Factor common terms from x^2 (3 x^2 + 1) - 2 (3 x^2 + 1).
Factor 3 x^2 + 1 from x^2 (3 x^2 + 1) - 2 (3 x^2 + 1):
Answer: (3 x^2 + 1) (x^2 - 2)
