Question

1. factor the expression: $5g^2 + 15g + 10$

a) $5(g + 2)(g + 1)$

b) $(5g + 10)(5g + 5)$

c) $5(g + 5)(g + 2)$

d) $5(g - 1)(g - 2)$

1. factor completely: $3n^2 - 15n + 18$

a) $(n - 2)(n - 3)$

b) $3(n + 2)(n + 3)$

c) $(3n - 9)(n - 2)$

d) $3(n - 3)(n - 2)$

1. factor $m^2 - 36$

a) $(m + 18)(m - 18)$

b) $(m + 6)^2$

c) $(m - 6)^2$

d) $(m + 6)(m - 6)$

1. factor $x^2 - 100$

a) $(x + 50)(x - 50)$

b) $(x + 10)(x - 10)$

c) $(x + 4)(x - 25)$

d) $(x - 10)^2$

1. factor the expression: $5g^2 + 15g + 10$

a) $5(g + 2)(g + 1)$

b) $(5g + 10)(5g + 5)$

c) $5(g + 5)(g + 2)$

d) $5(g - 1)(g - 2)$

Explanation:

Problem 16

Step1: Factor out GCF

$5g^2 + 15g + 10 = 5(g^2 + 3g + 2)$

Step2: Factor quadratic trinomial

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

Step3: Combine factors

$5(g+2)(g+1)$

Problem 17

Step1: Factor out GCF

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

Step2: Factor quadratic trinomial

$n^2 - 5n + 6 = (n-3)(n-2)$

Step3: Combine factors

$3(n-3)(n-2)$

Problem 18

Step1: Recognize difference of squares

$m^2 - 36 = m^2 - 6^2$

Step2: Apply difference of squares rule

$a^2 - b^2 = (a+b)(a-b)$, so $(m+6)(m-6)$

Problem 19

Step1: Recognize difference of squares

$x^2 - 100 = x^2 - 10^2$

Step2: Apply difference of squares rule

$a^2 - b^2 = (a+b)(a-b)$, so $(x+10)(x-10)$

Problem 20

Step1: Factor out GCF

$5g^2 + 15g + 10 = 5(g^2 + 3g + 2)$

Step2: Factor quadratic trinomial

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

Step3: Combine factors

$5(g+2)(g+1)$

Answer:

1. a) $5(g + 2)(g + 1)$
2. d) $3(n - 3)(n - 2)$
3. d) $(m + 6)(m - 6)$
4. b) $(x + 10)(x - 10)$
5. a) $5(g + 2)(g + 1)$