Question

algebra 1
assignment
factor the common factor out of each expression.

1. $-27n^5 - 18n$
2. $-4n^3 - 7n^5$
3. $10n^2 - 5n$
4. $-54x^4 + 45x$
5. $-12a^3 - 15a^2$
6. $-5r^4 + 3r^3 + 5r$
7. $16x^8 + 36 + 36x$
8. $49b^7 + 49b^4 + 7b^2$
9. $30k^3 + 48k^2 + 54k$
10. $16b^3 + 12b^2 + 14$

Explanation:

Step1: Identify GCF of terms

For $-27n^3 - 18n$: GCF of $-27, -18$ is $-9$; GCF of $n^3, n$ is $n$.

Step2: Factor out the GCF

$-9n(3n^2 + 2)$

Step1: Identify GCF of terms

For $-4n^3 - 7n^5$: GCF of $-4, -7$ is $-1$; GCF of $n^3, n^5$ is $n^3$.

Step2: Factor out the GCF

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

Step1: Identify GCF of terms

For $10n^2 - 5n$: GCF of $10, -5$ is $5$; GCF of $n^2, n$ is $n$.

Step2: Factor out the GCF

$5n(2n - 1)$

Step1: Identify GCF of terms

For $-54x^4 + 45x$: GCF of $-54, 45$ is $-9$; GCF of $x^4, x$ is $x$.

Step2: Factor out the GCF

$-9x(6x^3 - 5)$

Step1: Identify GCF of terms

For $-12a^3 - 15a^2$: GCF of $-12, -15$ is $-3$; GCF of $a^3, a^2$ is $a^2$.

Step2: Factor out the GCF

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

Step1: Identify GCF of terms

For $-5r^4 + 3r^3 + 5r$: GCF of $-5, 3, 5$ is $1$; GCF of $r^4, r^3, r$ is $r$.

Step2: Factor out the GCF

$r(-5r^3 + 3r^2 + 5)$

Step1: Identify GCF of terms

For $16x^8 + 36 + 36x$: GCF of $16, 36, 36$ is $4$.

Step2: Factor out the GCF

$4(4x^8 + 9 + 9x)$

Step1: Identify GCF of terms

For $49b^7 + 49b^4 + 7b^2$: GCF of $49, 49, 7$ is $7$; GCF of $b^7, b^4, b^2$ is $b^2$.

Step2: Factor out the GCF

$7b^2(7b^5 + 7b^2 + 1)$

Step1: Identify GCF of terms

For $30k^3 + 48k^2 + 54k$: GCF of $30, 48, 54$ is $6$; GCF of $k^3, k^2, k$ is $k$.

Step2: Factor out the GCF

$6k(5k^2 + 8k + 9)$

Step1: Identify GCF of terms

For $16b^3 + 12b^2 + 14$: GCF of $16, 12, 14$ is $2$.

Step2: Factor out the GCF

$2(8b^3 + 6b^2 + 7)$

Answer:

1. $\boldsymbol{-9n(3n^2 + 2)}$
2. $\boldsymbol{-n^3(4 + 7n^2)}$
3. $\boldsymbol{5n(2n - 1)}$
4. $\boldsymbol{-9x(6x^3 - 5)}$
5. $\boldsymbol{-3a^2(4a + 5)}$
6. $\boldsymbol{r(-5r^3 + 3r^2 + 5)}$
7. $\boldsymbol{4(4x^8 + 9 + 9x)}$
8. $\boldsymbol{7b^2(7b^5 + 7b^2 + 1)}$
9. $\boldsymbol{6k(5k^2 + 8k + 9)}$
10. $\boldsymbol{2(8b^3 + 6b^2 + 7)}$