Factor 4-14x^2-8x^4

Problem

4−14*x2−8*x4

Solution

1. Rearrange the expression into standard descending order of powers.

−8*x4−14*x2+4

2. Factor out the greatest common factor, which is −2

−2*(4*x4+7*x2−2)

3. Substitute a temporary variable to treat the expression as a quadratic. Let u=x2

−2*(4*u2+7*u−2)

4. Factor the quadratic expression 4*u2+7*u−2 by finding two numbers that multiply to −8 and add to 7 These numbers are 8 and −1

−2*(4*u2+8*u−u−2)

5. Group the terms to complete the factoring.

−2*(4*u*(u+2)−1*(u+2))

−2*(4*u−1)*(u+2)

6. Substitute back x2 for u

−2*(4*x2−1)*(x2+2)

7. Apply the difference of squares formula a2−b2=(a−b)*(a+b) to the factor (4*x2−1)

−2*(2*x−1)*(2*x+1)*(x2+2)

Final Answer

4−14*x2−8*x4=−2*(2*x−1)*(2*x+1)*(x2+2)

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