Question

4 $5x^3 + 6x^2 - 25x - 30$
5 $56k^3 + 21k^2 + 48k + 18$
6 $28n^3 - 16n^2 - 21n + 12$
7 $18ab - 15a - 6b + 5$
8 $24xy + 3x^2 + 8ry + rx$
9 $7uv + u + 21v^2 + 3v$
10 $30xy + 5x^2 + 12ny + 2nx$

Explanation:

Step1: Group terms for factoring

$5x^3 + 6x^2 -25x -30 = (5x^3 + 6x^2) + (-25x -30)$

Step2: Factor out GCF from groups

$= x^2(5x + 6) -5(5x + 6)$

Step3: Factor out common binomial

$= (x^2 -5)(5x + 6)$

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Step1: Group terms for factoring

$56k^3 + 21k^2 +48k +18 = (56k^3 + 21k^2) + (48k +18)$

Step2: Factor out GCF from groups

$= 7k^2(8k + 3) + 6(8k + 3)$

Step3: Factor out common binomial

$= (7k^2 +6)(8k + 3)$

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Step1: Group terms for factoring

$28n^3 -16n^2 -21n +12 = (28n^3 -16n^2) + (-21n +12)$

Step2: Factor out GCF from groups

$= 4n^2(7n -4) -3(7n -4)$

Step3: Factor out common binomial

$= (4n^2 -3)(7n -4)$

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Step1: Group terms for factoring

$18ab -15a -6b +5 = (18ab -15a) + (-6b +5)$

Step2: Factor out GCF from groups

$= 3a(6b -5) -1(6b -5)$

Step3: Factor out common binomial

$= (3a -1)(6b -5)$

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Step1: Rearrange and group terms

$24xy +3x^2 +8ry +rx = (3x^2 +24xy) + (rx +8ry)$

Step2: Factor out GCF from groups

$= 3x(x +8y) + r(x +8y)$

Step3: Factor out common binomial

$= (3x + r)(x +8y)$

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Step1: Rearrange and group terms

$7uv +u +21v^2 +3v = (7uv +21v^2) + (u +3v)$

Step2: Factor out GCF from groups

$= 7v(u +3v) +1(u +3v)$

Step3: Factor out common binomial

$= (7v +1)(u +3v)$

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Step1: Rearrange and group terms

$30xy +5x^2 +12ny +2nx = (5x^2 +30xy) + (2nx +12ny)$

Step2: Factor out GCF from groups

$= 5x(x +6y) + 2n(x +6y)$

Step3: Factor out common binomial

$= (5x +2n)(x +6y)$

Answer:

1. $(x^2 -5)(5x + 6)$
2. $(7k^2 +6)(8k + 3)$
3. $(4n^2 -3)(7n -4)$
4. $(3a -1)(6b -5)$
5. $(3x + r)(x +8y)$
6. $(7v +1)(u +3v)$
7. $(5x +2n)(x +6y)$