Question

Factor 6a2 - 8a - 30 completely

Answer 1

First separate out the common scalar factor 2 to get: 6a2−8a−30=2(3a2−4a−15)

Next find a pair of factors of 3×15=45 which differ by 4. The pair 9, 5 works.

Then you find:

3a2−4a−15=3a2−9a+5a−15=(3a2−9a)+(5a−15)=3a(a−3)+5(a−3)=(3a+5)(a−3)

Putting this all together:

6a2−8a−30=2(3a2−4a−15)=2(3a+5)(a−3)

Answer 2

6a^2 -8a -30
= 2 (3a^2 -4a -15)
= 2 (3a^2 -9a +5a -15)
= 2 {3a (a-3) +5 (a-3)}
= 2 (3a+5)(a-3)