Question

1. $(7h - 1)(-h - 9)$
2. $(3v + 2)(-6v^2 + 4v - 2)$
3. $(3x - 4)^2$

factor the greatest common factor out of each expression.

1. $50k^2 - 60k$
2. $7n^3 + 28n^5 - 49n^6$

directions: factor each completely. (4 points each)

1. $x^2 + 17x + 70$
2. $9n^2 - 11n + 2$
3. $9a^2 - 16$
4. $2h^2 + 5h + 3$

Explanation:

4) Step1: Apply distributive property (FOIL)

$(7h)(-h) + (7h)(-9) + (-1)(-h) + (-1)(-9)$

4) Step2: Simplify each term

$-7h^2 - 63h + h + 9$

4) Step3: Combine like terms

$-7h^2 - 62h + 9$

---

5) Step1: Distribute each term

$3v(-6v^2) + 3v(4v) + 3v(-2) + 2(-6v^2) + 2(4v) + 2(-2)$

5) Step2: Simplify each term

$-18v^3 + 12v^2 - 6v - 12v^2 + 8v - 4$

5) Step3: Combine like terms

$-18v^3 + 2v - 4$

---

6) Step1: Expand the squared binomial

$(3x - 4)(3x - 4)$

6) Step2: Apply distributive property

$3x(3x) + 3x(-4) + (-4)(3x) + (-4)(-4)$

6) Step3: Simplify and combine terms

$9x^2 - 12x - 12x + 16 = 9x^2 - 24x + 16$

---

7) Step1: Identify greatest common factor (GCF)

GCF of $50k^2$ and $60k$ is $10k$

7) Step2: Factor out the GCF

$10k(5k - 6)$

---

8) Step1: Identify greatest common factor (GCF)

GCF of $7n^3$, $28n^5$, $49n^6$ is $7n^3$

8) Step2: Factor out the GCF

$7n^3(1 + 4n^2 - 7n^3)$

---

9) Step1: Find pair of factors for 70

Factors of 70 that sum to 17: 7 and 10

9) Step2: Write factored form

$(x + 7)(x + 10)$

---

10) Step1: Split middle term

$9n^2 - 9n - 2n + 2$

10) Step2: Factor by grouping

$9n(n - 1) - 2(n - 1)$

10) Step3: Factor out common binomial

$(9n - 2)(n - 1)$

---

11) Step1: Recognize difference of squares

$9a^2 - 16 = (3a)^2 - (4)^2$

11) Step2: Apply difference of squares rule

$(3a + 4)(3a - 4)$

---

12) Step1: Split middle term

$2h^2 + 2h + 3h + 3$

12) Step2: Factor by grouping

$2h(h + 1) + 3(h + 1)$

12) Step3: Factor out common binomial

$(2h + 3)(h + 1)$

Answer:

1. $\boldsymbol{-7h^2 - 62h + 9}$
2. $\boldsymbol{-18v^3 + 2v - 4}$
3. $\boldsymbol{9x^2 - 24x + 16}$
4. $\boldsymbol{10k(5k - 6)}$
5. $\boldsymbol{7n^3(1 + 4n^2 - 7n^3)}$
6. $\boldsymbol{(x + 7)(x + 10)}$
7. $\boldsymbol{(9n - 2)(n - 1)}$
8. $\boldsymbol{(3a + 4)(3a - 4)}$
9. $\boldsymbol{(2h + 3)(h + 1)}$