1. $-21\times 2=-42$
$-21+2=-19$
$7x^2-21x+2x-6$
$7x(x-3)+2(x-3)$
$(x-3)(7x+2)$
2. $-6\times 4=-24$
$-6+4=-2$
$3n^2-6n+4n-8$
$3n(n-2)+4(n-2)$
$(n-2)(3n+4)$
3. $14\times 1=14$
$14+1=15$
$7b^2+14b+b+2$
$7b(b+2)+1(b+2)$
$(b+2)(7b+1)$
4. $-14\times 3=-42$
$-14+3=-11$
$21v^2-14v+3v-2$
$7v(3v-2)+1(3v-2)$
$(3v-2)(7v+1)$
5. $15\times -2=-30$
$15+-2=13$
$5a^2+15a-2a-6$
$5a(a+3)-2(a+3)$
$(a+3)(5a-2)$
6. $-20\times 2=-40$
$-20+2=-18$
$5n^2-20n+2n-8$
$5n(n-4)+2(n-4)$
$(n-4)(5n+2)$
7. $-1\times -4=4$
$-1+-4=-5$
$2x^2-x-4x+2$
$x(2x-1)-2(2x-1)$
$(2x-1)(x-2)$
8. $-6\times 2=-12$
$-6+2=-4$
$3r^2-6r+2r-4$
$3r(r-2)+2(r-2)$
$(r-2)(3r+2)$
9. $14\times 5=70$
$14+5=19$
$2x^2+14x+5x+35$
$2x(x+7)+5(x+7)$
$(x+7)(2x+5)$
10. $9\times -5=-45$
$9+-5=4$
$3x^2+9x-5x-15$
$3x(x+3)-5(x+3)$
$(x+3)(3x-5)$
11. $-3\times 2=-6$
$-3+2=-1$
$2b^2-3b+2b-3$
$b(2b-3)+1(2b-3)$
$(2b-3)(b+1)$
12. $8\times -3=-24$
$8+-3=5$
$2k^2+8k-3k-12$
$2k(k+4)-3(k+4)$
$(k+4)(2k-3)$
13. $15\times 2=30$
$15+2=17$
$3x^2+15xy+2xy+10y^2$
$3x(x+5y)+2y(x+5y)$
$(x+5y)(3x+2y)$
14. $-7\times 5=-35$
$-7+5=-2$
$7x^2-7xy+5xy-5y^2$
$7x(x-y)+5y(x-y)$
$(x-y)(7x+5y)$
15. $15\times -4=-60$
$15+-4=11$
$3x^2+15xy-4xy-20y^2$
$3x(x+5y)-4y(x+5y)$
$(x+5y)(3x-4y)$
16. $18\times -2=-36$
$18+-2=16$
$12u^2+18uv-2uv-3v^2$
$6u(2u+3v)-v(2u+3v)$
$(2u+3v)(6u-v)$
17. $-16\times -1=16$
$-16+-1=-17$
$4k^2-16k-k+4$
$4k(k-4)-1(k-4)$
$(k-4)(4k-1)$
18. $7\times -4=-28$
$7+-4=3$
$4r^2+7r-4r-7$
$r(4r+7)-1(4r+7)$
$(4r+7)(r-1)$
19. $-12\times 3=-36$
$-12+3=-9$
$4m^2-12mn+3mn-9n^2$
$4m(m-3n)+3n(m-3n)$
$(m-3n)(4m+3n)$
20. $\text{Cannot be factored.}$
21. $12\times 1=12$
$12+1=13$
$4x^2+12xy+xy+3y^2$
$4x(x+3y)+y(x+3y)$
$(x+3y)(4x+y)$
22. $8\times -3=-24$
$8+-3=5$
$6u^2+8uv-3uv-4v^2$
$2u(3u+4v)-v(3u+4v)$
$(3u+4v)(2u-v)$
23. $20\times -1=-20$
$20+-1=19$
$10x^2+20xy-xy-2y^2$
$10x(x+2y)-1(x+2y)$
$(x-2y)(10x-y)$
24. $-15\times 2=-30$
$-15+2=-13$
$6x^2-15xy+2xy-5y^2$
$3x(2x-5y)+y(2x-5y)$
$(2x-5y)(3x+y)$