Question

algebra 1
quiz practice
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factor the common factor out of each expression.

1. $100v + 90$
2. $64z - 72$
3. $3n^2 + 9n$
4. $5r^2 - 45r$
5. $15x^2 - 25x - 50$
6. $8 + 4x + 8x^3$

factor each difference of squares completely.

1. $m^2 - 4$
2. $4n^2 - 1$
3. $25b^2 - 9$
4. $9a^2 - 16$

factor each trinomial completely.

1. $v^2 + 13v + 40$
2. $v^2 + 3v - 54$
3. $p^2 - 12p + 32$
4. $n^2 + 4n - 45$
5. $5v^2 - 40v - 45$
6. $2v^2 + 6v - 36$

Explanation:

Step1: Factor out GCF (1)

Find GCF of 100,90: $10$.
$100v + 90 = 10(10v + 9)$

Step2: Factor out GCF (2)

Find GCF of 64,72: $8$.
$64x - 72 = 8(8x - 9)$

Step3: Factor out GCF (3)

Find GCF of $3n^2,9n$: $3n$.
$3n^2 + 9n = 3n(n + 3)$

Step4: Factor out GCF (4)

Find GCF of $5r^2,45r$: $5r$.
$5r^2 - 45r = 5r(r - 9)$

Step5: Factor out GCF (5)

Find GCF of $15x^2,25x,50$: $5$.
$15x^2 - 25x - 50 = 5(3x^2 - 5x - 10)$

Step6: Factor out GCF (6)

Find GCF of 8,4x,$8x^3$: $4$.
$8 + 4x + 8x^3 = 4(2 + x + 2x^3)$

Step7: Factor difference of squares (7)

Use $a^2-b^2=(a+b)(a-b)$.
$m^2 - 4 = m^2 - 2^2 = (m + 2)(m - 2)$

Step8: Factor difference of squares (8)

Use $a^2-b^2=(a+b)(a-b)$.
$4n^2 - 1 = (2n)^2 - 1^2 = (2n + 1)(2n - 1)$

Step9: Factor difference of squares (9)

Use $a^2-b^2=(a+b)(a-b)$.
$25b^2 - 9 = (5b)^2 - 3^2 = (5b + 3)(5b - 3)$

Step10: Factor difference of squares (10)

Use $a^2-b^2=(a+b)(a-b)$.
$9a^2 - 16 = (3a)^2 - 4^2 = (3a + 4)(3a - 4)$

Step11: Factor trinomial (11)

Find pair: 5,8 (sum=13, product=40).
$v^2 + 13v + 40 = (v + 5)(v + 8)$

Step12: Factor trinomial (12)

Find pair: 9,-6 (sum=3, product=-54).
$v^2 + 3v - 54 = (v + 9)(v - 6)$

Step13: Factor trinomial (13)

Find pair: -4,-8 (sum=-12, product=32).
$p^2 - 12p + 32 = (p - 4)(p - 8)$

Step14: Factor trinomial (14)

Find pair: 9,-5 (sum=4, product=-45).
$n^2 + 4n - 45 = (n + 9)(n - 5)$

Step15: Factor trinomial (15)

First factor out GCF=5: $5(v^2 - 8v - 9)$.
Find pair: -9,1 (sum=-8, product=-9).
$5(v^2 - 8v - 9) = 5(v - 9)(v + 1)$

Step16: Factor trinomial (16)

First factor out GCF=2: $2(v^2 + 3v - 18)$.
Find pair: 6,-3 (sum=3, product=-18).
$2(v^2 + 3v - 18) = 2(v + 6)(v - 3)$

Answer:

1. $10(10v + 9)$
2. $8(8x - 9)$
3. $3n(n + 3)$
4. $5r(r - 9)$
5. $5(3x^2 - 5x - 10)$
6. $4(2 + x + 2x^3)$
7. $(m + 2)(m - 2)$
8. $(2n + 1)(2n - 1)$
9. $(5b + 3)(5b - 3)$
10. $(3a + 4)(3a - 4)$
11. $(v + 5)(v + 8)$
12. $(v + 9)(v - 6)$
13. $(p - 4)(p - 8)$
14. $(n + 9)(n - 5)$
15. $5(v - 9)(v + 1)$
16. $2(v + 6)(v - 3)$