How do you factor a^4-2a^2-48?

1 Answer
Jun 30, 2018

(a^2-8)(a^2+6)

Explanation:

Re-write the equation as:

((a^4) - (2a^2)) - 48

Trying to factor by splitting middle term:

Step 1: Find two factors of -48 whose sum equals the coefficient of the middle term, which is -2.

-8 + 6 = -2

and

-8 xx 6 = -48

Step 2: Rewrite the polynomial splitting the middle term using the two factors found in step 1 above, -8 and 6

a^4 -8a^2+6a^2-48

Step 3: Pull out the common factor

a^2(a^2-8) + 6(a^2-8)

(a^2-8)(a^2+6) ----> desired factors!