New problem I am having difficulties with

[Ravingsofthesane]

Hello everyone , hope it is a good day for you all.

Here is the problem I am having issues with


Factor Completly

6(a+2)^2-7(a+2)-5

I belive that I may be starting completely wrong with this.

what I have done is this to solve the problem

1. 6(A^2+2A+2A+4) - 7A+2-5

2. 6A^2 + 12A + 12A +24 - 7A + 2 - 5

3. 6A^2 + 17A + 21


then you factor that result out

is this correct or did I miss something?



thanks again

 

[soroban]

Hello, Ravings!

Yes, you missed something . . .

Factor completly: .6(a + 2)² - 7(a + 2) - 5
.

By writing the problem in that strange form, they did us a favor.


Note that (a + 2) shows up twice . . . replace it with X.

We have: .6X² - 7X - 5 . . . which factors: .(2X + 1)(3X - 5) . . . . There!

Back-substitute: .(2[a + 2] + 1) (3[a + 2] - 5)

And tidy-up: .(2a + 4 + 1)(3a + 6 - 5) .= .(2a + 5)(3a + 1)