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

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Answer 1 · 2018-06-30T06:34:52

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

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!