Question

integrated math ii
factoring test 1 review
factor the common factor out of each expression.

1. - 5a² + 15a - 20
2. 2 + 2k+4k³
3. - 3n + 3
4. 25x⁹ + 20x⁵ + 15x⁴
5. 6n² + 3n + 3
6. 2a⁴ + 10a² + 8a - 10
7. 2 + 2p
8. 12p⁴ + 3p² + 6

Explanation:

Step1: Find GCF for -5a² + 15a - 20

The GCF of -5, 15 and -20 is 5.
$-5a^{2}+15a - 20=-5(a^{2}-3a + 4)$

Step2: Find GCF for 2 + 2k+4k³

The GCF of 2, 2 and 4 is 2.
$2 + 2k+4k^{3}=2(1 + k + 2k^{3})$

Step3: Find GCF for -3n + 3

The GCF of -3 and 3 is 3.
$-3n + 3=3(-n + 1)$

Step4: Find GCF for 25x⁹+20x⁵+15x⁴

The GCF of 25, 20 and 15 is 5, and the lowest - power of x is x⁴.
$25x^{9}+20x^{5}+15x^{4}=5x^{4}(5x^{5}+4x + 3)$

Step5: Find GCF for 6n²+3n + 3

The GCF of 6, 3 and 3 is 3.
$6n^{2}+3n + 3=3(2n^{2}+n + 1)$

Step6: Find GCF for 2a⁴+10a²+8a - 10

The GCF of 2, 10, 8 and - 10 is 2.
$2a^{4}+10a^{2}+8a - 10=2(a^{4}+5a^{2}+4a - 5)$

Step7: Find GCF for 2 + 2p

The GCF of 2 and 2 is 2.
$2 + 2p=2(1 + p)$

Step8: Find GCF for 12p⁴+3p²+6

The GCF of 12, 3 and 6 is 3.
$12p^{4}+3p^{2}+6=3(4p^{4}+p^{2}+2)$

Answer:

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