Question

1. $2n^{2}+6n - 108$
2. $5n^{2}+10n + 20$
3. $2k^{2}+22k + 60$
4. $a^{2}-a - 90$
5. $p^{2}+11p + 10$
6. $5v^{2}-30v + 40$
7. $2p^{2}+2p - 4$
8. $4v^{2}-4v - 8$
9. $x^{2}-15x + 50$
10. $v^{2}-7v + 10$
11. $p^{2}+3p - 18$
12. $6v^{2}+66v + 60$

Explanation:

15) Step1: Factor out GCF 2

$2(n^2 + 3n - 54)$

15) Step2: Factor quadratic trinomial

Find two numbers: $9$ and $-6$ (sum $3$, product $-54$)
$2(n + 9)(n - 6)$

16) Step1: Factor out GCF 5

$5(n^2 + 2n + 4)$

16) Step2: Check for further factoring

Quadratic has no real factors, so stop.

17) Step1: Factor out GCF 2

$2(k^2 + 11k + 30)$

17) Step2: Factor quadratic trinomial

Find two numbers: $6$ and $5$ (sum $11$, product $30$)
$2(k + 6)(k + 5)$

18) Step1: Factor quadratic trinomial

Find two numbers: $9$ and $-10$ (sum $-1$, product $-90$)
$(a + 9)(a - 10)$

19) Step1: Factor quadratic trinomial

Find two numbers: $10$ and $1$ (sum $11$, product $10$)
$(p + 10)(p + 1)$

20) Step1: Factor out GCF 5

$5(v^2 - 6v + 8)$

20) Step2: Factor quadratic trinomial

Find two numbers: $-2$ and $-4$ (sum $-6$, product $8$)
$5(v - 2)(v - 4)$

21) Step1: Factor out GCF 2

$2(p^2 + p - 2)$

21) Step2: Factor quadratic trinomial

Find two numbers: $2$ and $-1$ (sum $1$, product $-2$)
$2(p + 2)(p - 1)$

22) Step1: Factor out GCF 4

$4(v^2 - v - 2)$

22) Step2: Factor quadratic trinomial

Find two numbers: $1$ and $-2$ (sum $-1$, product $-2$)
$4(v + 1)(v - 2)$

23) Step1: Factor quadratic trinomial

Find two numbers: $-5$ and $-10$ (sum $-15$, product $50$)
$(x - 5)(x - 10)$

24) Step1: Factor quadratic trinomial

Find two numbers: $-2$ and $-5$ (sum $-7$, product $10$)
$(v - 2)(v - 5)$

25) Step1: Factor quadratic trinomial

Find two numbers: $6$ and $-3$ (sum $3$, product $-18$)
$(p + 6)(p - 3)$

26) Step1: Factor out GCF 6

$6(v^2 + 11v + 10)$

26) Step2: Factor quadratic trinomial

Find two numbers: $10$ and $1$ (sum $11$, product $10$)
$6(v + 10)(v + 1)$

Answer:

1. $2(n + 9)(n - 6)$
2. $5(n^2 + 2n + 4)$
3. $2(k + 6)(k + 5)$
4. $(a + 9)(a - 10)$
5. $(p + 10)(p + 1)$
6. $5(v - 2)(v - 4)$
7. $2(p + 2)(p - 1)$
8. $4(v + 1)(v - 2)$
9. $(x - 5)(x - 10)$
10. $(v - 2)(v - 5)$
11. $(p + 6)(p - 3)$
12. $6(v + 10)(v + 1)$