Question

1. $7w^{5}-35w^{2}$
2. $24p^{3}+15p^{2}-56p - 35$
3. $16x^{2}+8$
4. $24r^{3}-64r^{2}-21r + 56$
5. $4x(3x - 1)+5(3x - 1)$
6. $49x^{3}-35x^{2}+56x - 40$

Explanation:

Problem 5: $7w^5 - 35w^2$

Step1: Factor out GCF

Identify greatest common factor (GCF) of terms: $7w^2$.
$7w^5 - 35w^2 = 7w^2(w^3 - 5)$

Problem 6: $16x^2 + 8$

Step1: Factor out GCF

Identify GCF of terms: $8$.
$16x^2 + 8 = 8(2x^2 + 1)$

Problem 7: $4x(3x - 1) + 5(3x - 1)$

Step1: Factor out common binomial

Identify common binomial factor: $(3x-1)$.
$4x(3x - 1) + 5(3x - 1) = (3x-1)(4x+5)$

Problem 12: $24p^3 + 15p^2 - 56p - 35$

Step1: Group terms for factoring

Split into two pairs of terms.
$(24p^3 + 15p^2) + (-56p - 35)$

Step2: Factor GCF from each group

Factor GCF from each pair.
$3p^2(8p + 5) - 7(8p + 5)$

Step3: Factor out common binomial

Factor out shared binomial $(8p+5)$.
$(8p+5)(3p^2 - 7)$

Problem 13: $24r^3 - 64r^2 - 21r + 56$

Step1: Group terms for factoring

Split into two pairs of terms.
$(24r^3 - 64r^2) + (-21r + 56)$

Step2: Factor GCF from each group

Factor GCF from each pair.
$8r^2(3r - 8) - 7(3r - 8)$

Step3: Factor out common binomial

Factor out shared binomial $(3r-8)$.
$(3r-8)(8r^2 - 7)$

Problem 14: $49x^3 - 35x^2 + 56x - 40$

Step1: Group terms for factoring

Split into two pairs of terms.
$(49x^3 - 35x^2) + (56x - 40)$

Step2: Factor GCF from each group

Factor GCF from each pair.
$7x^2(7x - 5) + 8(7x - 5)$

Step3: Factor out common binomial

Factor out shared binomial $(7x-5)$.
$(7x-5)(7x^2 + 8)$

Answer:

1. $7w^2(w^3 - 5)$
2. $8(2x^2 + 1)$
3. $(3x-1)(4x+5)$
4. $(8p+5)(3p^2 - 7)$
5. $(3r-8)(8r^2 - 7)$
6. $(7x-5)(7x^2 + 8)$