Question

algebra 2
name
factor trinomials a = 1
factor each completely.

1. $5p^3 - 30p^2 - 35p$
2. $p^2 + 5p + 6$
3. $r^3 - 3r^2 - 54r$
4. $n^2 - 12n + 32$
5. $5a^2 - 40a - 45$
6. $6x^2 + 18x$
7. $2m^2 + 14m - 36$
8. $n^2 + 7n - 18$
9. $4b^3 + 36b^2 - 40b$
10. $2a^4 - 30a^3 + 108a^2$
11. $a^3 + 2a^2 + a$
12. $m^2 + 6m - 27$
13. $2x^3 - 16x^2 - 40x$
14. $6n^3 - 36n^2 - 240n$
15. $a^2 - 2a - 8$
16. $b^2 - 4b - 5$
17. $n^2 - 6n - 40$
18. $n^3 - 6n^2 - 27n$
19. $r^2 - 3r$
20. $b^2 - 7b$

Explanation:

Step1: Factor out GCF first

$5p^3 - 30p^2 - 35p = 5p(p^2 - 6p - 7)$

Step2: Factor the quadratic

$5p(p^2 - 6p - 7) = 5p(p - 7)(p + 1)$

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Step1: Factor the quadratic directly

$p^2 + 5p + 6 = (p + 2)(p + 3)$

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Step1: Factor out GCF first

$r^3 - 3r^2 - 54r = r(r^2 - 3r - 54)$

Step2: Factor the quadratic

$r(r^2 - 3r - 54) = r(r - 9)(r + 6)$

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Step1: Factor the quadratic directly

$n^2 - 12n + 32 = (n - 4)(n - 8)$

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Step1: Factor out GCF first

$5a^2 - 40a - 45 = 5(a^2 - 8a - 9)$

Step2: Factor the quadratic

$5(a^2 - 8a - 9) = 5(a - 9)(a + 1)$

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Step1: Factor out GCF directly

$6x^2 + 18x = 6x(x + 3)$

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Step1: Factor out GCF first

$2m^2 + 14m - 36 = 2(m^2 + 7m - 18)$

Step2: Factor the quadratic

$2(m^2 + 7m - 18) = 2(m + 9)(m - 2)$

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Step1: Factor the quadratic directly

$n^2 + 7n - 18 = (n + 9)(n - 2)$

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Step1: Factor out GCF first

$4b^3 + 36b^2 - 40b = 4b(b^2 + 9b - 10)$

Step2: Factor the quadratic

$4b(b^2 + 9b - 10) = 4b(b + 10)(b - 1)$

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Step1: Factor out GCF first

$2a^4 - 30a^3 + 108a^2 = 2a^2(a^2 - 15a + 54)$

Step2: Factor the quadratic

$2a^2(a^2 - 15a + 54) = 2a^2(a - 6)(a - 9)$

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Step1: Factor out GCF first

$a^3 + 2a^2 + a = a(a^2 + 2a + 1)$

Step2: Factor perfect square quadratic

$a(a^2 + 2a + 1) = a(a + 1)^2$

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Step1: Factor the quadratic directly

$m^2 + 6m - 27 = (m + 9)(m - 3)$

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Step1: Factor out GCF first

$2x^3 - 16x^2 - 40x = 2x(x^2 - 8x - 20)$

Step2: Factor the quadratic

$2x(x^2 - 8x - 20) = 2x(x - 10)(x + 2)$

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Step1: Factor out GCF first

$6n^3 - 36n^2 - 240n = 6n(n^2 - 6n - 40)$

Step2: Factor the quadratic

$6n(n^2 - 6n - 40) = 6n(n - 10)(n + 4)$

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Step1: Factor the quadratic directly

$a^2 - 2a - 8 = (a - 4)(a + 2)$

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Step1: Factor the quadratic directly

$b^2 - 4b - 5 = (b - 5)(b + 1)$

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Step1: Factor the quadratic directly

$n^2 - 6n - 40 = (n - 10)(n + 4)$

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Step1: Factor out GCF first

$n^3 - 6n^2 - 27n = n(n^2 - 6n - 27)$

Step2: Factor the quadratic

$n(n^2 - 6n - 27) = n(n - 9)(n + 3)$

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Step1: Factor out GCF directly

$r^2 - 3r = r(r - 3)$

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Step1: Factor out GCF directly

$b^2 - 7b = b(b - 7)$

Answer:

1. $5p(p - 7)(p + 1)$
2. $(p + 2)(p + 3)$
3. $r(r - 9)(r + 6)$
4. $(n - 4)(n - 8)$
5. $5(a - 9)(a + 1)$
6. $6x(x + 3)$
7. $2(m + 9)(m - 2)$
8. $(n + 9)(n - 2)$
9. $4b(b + 10)(b - 1)$
10. $2a^2(a - 6)(a - 9)$
11. $a(a + 1)^2$
12. $(m + 9)(m - 3)$
13. $2x(x - 10)(x + 2)$
14. $6n(n - 10)(n + 4)$
15. $(a - 4)(a + 2)$
16. $(b - 5)(b + 1)$
17. $(n - 10)(n + 4)$
18. $n(n - 9)(n + 3)$
19. $r(r - 3)$
20. $b(b - 7)$