Question

1. $5x^3 - 10$
2. $15x - 20y$
3. $8ab^2 - 12a^2b^3$
4. $7w^5 - 35w^2$
5. $16x^2 + 8$
6. $4x(3x - 1) + 5(3x - 1)$
7. $6v^3 - 16v^2 + 21v - 56$
8. $21k^3 - 84k^2 + 15k - 60$
9. $25v^3 + 5v^2 + 30v + 6$
10. $24p^3 + 15p^2 - 56p - 35$
11. $24r^3 - 64r^2 - 21r + 56$
12. $49x^3 - 35x^2 + 56x - 40$

Explanation:

Step1: Factor out GCF of $5x^3-10$

$\boldsymbol{5(x^3 - 2)}$

Step2: Factor out GCF of $15x-20y$

$\boldsymbol{5(3x - 4y)}$

Step3: Factor out GCF of $8ab^2-12a^2b^3$

$\boldsymbol{4ab^2(2 - 3ab)}$

Step4: Factor out GCF of $7w^5-35w^2$

$\boldsymbol{7w^2(w^3 - 5)}$

Step5: Factor out GCF of $16x^2+8$

$\boldsymbol{8(2x^2 + 1)}$

Step6: Factor out binomial GCF of $4x(3x-1)+5(3x-1)$

$\boldsymbol{(3x - 1)(4x + 5)}$

Step7: Group & factor $6v^3-16v^2+21v-56$

$\boldsymbol{2v^2(3v-8)+7(3v-8)=(3v-8)(2v^2+7)}$

Step8: Group & factor $21k^3-84k^2+15k-60$

$\boldsymbol{21k^2(k-4)+15(k-4)=3(k-4)(7k^2+5)}$

Step9: Group & factor $25v^3+5v^2+30v+6$

$\boldsymbol{5v^2(5v+1)+6(5v+1)=(5v+1)(5v^2+6)}$

Step10: Group & factor $24p^3+15p^2-56p-35$

$\boldsymbol{3p^2(8p+5)-7(8p+5)=(8p+5)(3p^2-7)}$

Step11: Group & factor $24r^3-64r^2-21r+56$

$\boldsymbol{8r^2(3r-8)-7(3r-8)=(3r-8)(8r^2-7)}$

Step12: Group & factor $49x^3-35x^2+56x-40$

$\boldsymbol{7x^2(7x-5)+8(7x-5)=(7x-5)(7x^2+8)}$

Answer:

1. $5(x^3 - 2)$
2. $5(3x - 4y)$
3. $4ab^2(2 - 3ab)$
4. $7w^2(w^3 - 5)$
5. $8(2x^2 + 1)$
6. $(3x - 1)(4x + 5)$
7. $(3v - 8)(2v^2 + 7)$
8. $3(k - 4)(7k^2 + 5)$
9. $(5v + 1)(5v^2 + 6)$
10. $(8p + 5)(3p^2 - 7)$
11. $(3r - 8)(8r^2 - 7)$
12. $(7x - 5)(7x^2 + 8)$