Question

set 3

1. $a^2 - 2a - 3$
2. $x^2 - 7x - 30$
3. $b^2 - 2b - 63$
4. $k^2 - 12k - 64$

set 4

1. $x^2 - 11x + 24$
2. $x^2 - 14x + 49$
3. $y^2 - 17y + 72$
4. $m^2 - 15m + 50$

mixed practice

1. $a^2 + 6a - 16$
2. $x^2 - 14x - 72$
3. $y^2 + 13y + 40$
4. $w^2 - 16w + 48$
5. $n^2 - n - 30$
6. $k^2 + 13k + 42$

examples with a gcf
directions: look for a gcf first, then factor the remaining trinomial.

1. $4k^2 + 12k + 8$
2. $2x^2 - 8x - 24$
3. $3y^2 - 15y + 12$
4. $3a^3 + 30a^2 + 63a$
5. $2b^2 + 10b + 12$
6. $5x^2y - 15xy - 140y$

Explanation:

SET 3

Problem 9: Factor $a^2-2a-3$

Step1: Find pair: sum=-2, product=-3

The pair is $1$ and $-3$.

Step2: Write factored form

$(a+1)(a-3)$

Problem10: Factor $x^2-7x-30$

Step1: Find pair: sum=-7, product=-30

The pair is $3$ and $-10$.

Step2: Write factored form

$(x+3)(x-10)$

Problem11: Factor $b^2-2b-63$

Step1: Find pair: sum=-2, product=-63

The pair is $7$ and $-9$.

Step2: Write factored form

$(b+7)(b-9)$

Problem12: Factor $k^2-12k-64$

Step1: Find pair: sum=-12, product=-64

The pair is $4$ and $-16$.

Step2: Write factored form

$(k+4)(k-16)$

SET 4

Problem13: Factor $x^2-11x+24$

Step1: Find pair: sum=-11, product=24

The pair is $-3$ and $-8$.

Step2: Write factored form

$(x-3)(x-8)$

Problem14: Factor $x^2-14x+49$

Step1: Identify perfect square trinomial

$(-7)^2=49$, $2*(-7)=-14$

Step2: Write factored form

$(x-7)^2$

Problem15: Factor $y^2-17y+72$

Step1: Find pair: sum=-17, product=72

The pair is $-8$ and $-9$.

Step2: Write factored form

$(y-8)(y-9)$

Problem16: Factor $m^2-15m+50$

Step1: Find pair: sum=-15, product=50

The pair is $-5$ and $-10$.

Step2: Write factored form

$(m-5)(m-10)$

MIXED PRACTICE

Problem17: Factor $a^2+6a-16$

Step1: Find pair: sum=6, product=-16

The pair is $8$ and $-2$.

Step2: Write factored form

$(a+8)(a-2)$

Problem18: Factor $x^2-14x-72$

Step1: Find pair: sum=-14, product=-72

The pair is $4$ and $-18$.

Step2: Write factored form

$(x+4)(x-18)$

Problem19: Factor $y^2+13y+40$

Step1: Find pair: sum=13, product=40

The pair is $5$ and $8$.

Step2: Write factored form

$(y+5)(y+8)$

Problem20: Factor $w^2-16w+48$

Step1: Find pair: sum=-16, product=48

The pair is $-4$ and $-12$.

Step2: Write factored form

$(w-4)(w-12)$

Problem21: Factor $n^2-n-30$

Step1: Find pair: sum=-1, product=-30

The pair is $5$ and $-6$.

Step2: Write factored form

$(n+5)(n-6)$

Problem22: Factor $k^2+13k+42$

Step1: Find pair: sum=13, product=42

The pair is $6$ and $7$.

Step2: Write factored form

$(k+6)(k+7)$

EXAMPLES WITH A GCF

Problem23: Factor $4k^2+12k+8$

Step1: Factor out GCF=4

$4(k^2+3k+2)$

Step2: Factor the trinomial

$4(k+1)(k+2)$

Problem24: Factor $2x^2-8x-24$

Step1: Factor out GCF=2

$2(x^2-4x-12)$

Step2: Factor the trinomial

$2(x+2)(x-6)$

Problem25: Factor $3y^2-15y+12$

Step1: Factor out GCF=3

$3(y^2-5y+4)$

Step2: Factor the trinomial

$3(y-1)(y-4)$

Problem26: Factor $3a^3+30a^2+63a$

Step1: Factor out GCF=3a

$3a(a^2+10a+21)$

Step2: Factor the trinomial

$3a(a+3)(a+7)$

Problem27: Factor $2b^2+10b+12$

Step1: Factor out GCF=2

$2(b^2+5b+6)$

Step2: Factor the trinomial

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

Problem28: Factor $5x^2y-15xy-140y$

Step1: Factor out GCF=5y

$5y(x^2-3x-28)$

Step2: Factor the trinomial

$5y(x+4)(x-7)$

Answer:

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