Question

Factor by grouping

NEED HELP ASAP
# after letters are the exponent
1: 28v+16v2-21v-12
2: 49x3-35x2+56x-40
3: 24r3-64r2-21r+56

Answer 1

Answer and step-by-step explanation:

`28v^3 +16v^2-21v-12 =` collecting
`4v^2` in the first two terms and
`-3` in the last two:

`4v^2(7v+4)-3(7v+4) =` collecting the bracket

`(7v+4)(4v^2-3)`

Bonus stage: if you are factoring over the real numbers and not over the rational, the second brackets is a difference of squares. Else, you stop here.

`(7v+4)(2v+\sqrt3)(2v-\sqrt3)`

NEXT!

`49x^3-35x^2+56x-40=`As before,
`7x^2`in the first two, and
`8` in the last two:

`7x^2(7x-5)-8(7x-5)` collecting the bracket again

`(7x-5)(7x^2-8) =`again, bonus step

`(7x-5)(\sqrt7 x +2\sqrt2) (\sqrt7x-2\sqrt2)`

FINALLY!

`24r^3-64r^2-21r+56 =\\8r^2(3r-8) -7(3r-8)=\\(3r-8)(8r^2-7) =`Again, bonus step

`(3r-8)(2\sqrt2r+\sqrt7)(2\sqrt2r-\sqrt7)`

Since usually most courses talk about factorization of polynomials BEFORE talking about real numbers, I would stop at the third stage, skipping the fourth.