Answer and step-by-step explanation:
[tex]28v^3 +16v^2-21v-12 =[/tex] collecting [tex]4v^2[/tex] in the first two terms and [tex]-3[/tex] in the last two:
[tex]4v^2(7v+4)-3(7v+4) =[/tex] collecting the bracket
[tex](7v+4)(4v^2-3)[/tex]
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.
[tex](7v+4)(2v+\sqrt3)(2v-\sqrt3)[/tex]
NEXT!
[tex]49x^3-35x^2+56x-40=[/tex]As before, [tex]7x^2[/tex]in the first two, and [tex]8[/tex] in the last two:
[tex]7x^2(7x-5)-8(7x-5)[/tex] collecting the bracket again
[tex](7x-5)(7x^2-8) =[/tex]again, bonus step
[tex](7x-5)(\sqrt7 x +2\sqrt2) (\sqrt7x-2\sqrt2)[/tex]
FINALLY!
[tex]24r^3-64r^2-21r+56 =\\8r^2(3r-8) -7(3r-8)=\\(3r-8)(8r^2-7) =[/tex]Again, bonus step
[tex](3r-8)(2\sqrt2r+\sqrt7)(2\sqrt2r-\sqrt7)[/tex]
Since usually most courses talk about factorization of polynomials BEFORE talking about real numbers, I would stop at the third stage, skipping the fourth.
