Question

algebra i
assignment
factor each completely.

1. $9n^3 - 3n^2 - 21n + 7$
2. $12a^3 + 3a^2 + 20a + 5$
3. $28a^3 + 49a^2 - 32a - 56$
4. $8x^3 - 10x^2 + 28x - 35$
5. $7p^3 + p^2 + 42p + 6$
6. $12x^3 + 14x^2 - 30x - 35$
7. $6m^3 + 5m^2 - 18m - 15$
8. $28k^3 - 8k^2 - 35k + 10$
9. $x^3 - 5x^2 - 5x + 25$
10. $8x^3 - 8x^2 - x + 1$

Explanation:

1) Problem 1: $9n^3 - 3n^2 -21n +7$

Step1: Group first/last two terms

$(9n^3 - 3n^2) + (-21n +7)$

Step2: Factor out GCF from groups

$3n^2(3n - 1) -7(3n - 1)$

Step3: Factor out common binomial

$(3n - 1)(3n^2 -7)$

2) Problem 2: $12a^3 + 3a^2 +20a +5$

Step1: Group first/last two terms

$(12a^3 + 3a^2) + (20a +5)$

Step2: Factor out GCF from groups

$3a^2(4a + 1) +5(4a + 1)$

Step3: Factor out common binomial

$(4a + 1)(3a^2 +5)$

3) Problem 3: $28a^3 + 49a^2 -32a -56$

Step1: Group first/last two terms

$(28a^3 + 49a^2) + (-32a -56)$

Step2: Factor out GCF from groups

$7a^2(4a + 7) -8(4a + 7)$

Step3: Factor out common binomial

$(4a + 7)(7a^2 -8)$

4) Problem 4: $8x^3 -10x^2 +28x -35$

Step1: Group first/last two terms

$(8x^3 -10x^2) + (28x -35)$

Step2: Factor out GCF from groups

$2x^2(4x - 5) +7(4x - 5)$

Step3: Factor out common binomial

$(4x - 5)(2x^2 +7)$

5) Problem 5: $7p^3 + p^2 +42p +6$

Step1: Group first/last two terms

$(7p^3 + p^2) + (42p +6)$

Step2: Factor out GCF from groups

$p^2(7p + 1) +6(7p + 1)$

Step3: Factor out common binomial

$(7p + 1)(p^2 +6)$

6) Problem 6: $12x^3 +14x^2 -30x -35$

Step1: Group first/last two terms

$(12x^3 +14x^2) + (-30x -35)$

Step2: Factor out GCF from groups

$2x^2(6x + 7) -5(6x + 7)$

Step3: Factor out common binomial

$(6x + 7)(2x^2 -5)$

7) Problem 7: $6m^3 +5m^2 -18m -15$

Step1: Group first/last two terms

$(6m^3 +5m^2) + (-18m -15)$

Step2: Factor out GCF from groups

$m^2(6m + 5) -3(6m + 5)$

Step3: Factor out common binomial

$(6m + 5)(m^2 -3)$

8) Problem 8: $28k^3 -8k^2 -35k +10$

Step1: Group first/last two terms

$(28k^3 -8k^2) + (-35k +10)$

Step2: Factor out GCF from groups

$4k^2(7k - 2) -5(7k - 2)$

Step3: Factor out common binomial

$(7k - 2)(4k^2 -5)$

9) Problem 9: $x^3 -5x^2 -5x +25$

Step1: Group first/last two terms

$(x^3 -5x^2) + (-5x +25)$

Step2: Factor out GCF from groups

$x^2(x - 5) -5(x - 5)$

Step3: Factor out common binomial

$(x - 5)(x^2 -5)$

10) Problem 10: $8x^3 -8x^2 -x +1$

Step1: Group first/last two terms

$(8x^3 -8x^2) + (-x +1)$

Step2: Factor out GCF from groups

$8x^2(x - 1) -1(x - 1)$

Step3: Factor out common binomial

$(x - 1)(8x^2 -1)$

Answer:

1. $\boldsymbol{(3n - 1)(3n^2 -7)}$
2. $\boldsymbol{(4a + 1)(3a^2 +5)}$
3. $\boldsymbol{(4a + 7)(7a^2 -8)}$
4. $\boldsymbol{(4x - 5)(2x^2 +7)}$
5. $\boldsymbol{(7p + 1)(p^2 +6)}$
6. $\boldsymbol{(6x + 7)(2x^2 -5)}$
7. $\boldsymbol{(6m + 5)(m^2 -3)}$
8. $\boldsymbol{(7k - 2)(4k^2 -5)}$
9. $\boldsymbol{(x - 5)(x^2 -5)}$
10. $\boldsymbol{(x - 1)(8x^2 -1)}$