Question

review
find the gcf of the following terms.

1. 4 and 6x
2. 10x² and 20x
3. 9x⁴ and 6x⁶

gcf factoring
factor out the gcf of the following expressions.

1. 2 + 4x
2. 15x + 5x²
3. 6n⁵ + 10n
4. 8x³ + 4
5. 7y⁵ + 7y³
6. 12x⁴ + 18x²

Explanation:

Step1: Find GCF of 4 and 6x

Prime factors: $4=2^2$, $6x=2\times3\times x$. GCF is $2$.

Step2: Find GCF of $10x^2$ and $20x$

Prime factors: $10x^2=2\times5\times x^2$, $20x=2^2\times5\times x$. GCF is $2\times5\times x=10x$.

Step3: Find GCF of $9x^4$ and $6x^6$

Prime factors: $9x^4=3^2\times x^4$, $6x^6=2\times3\times x^6$. GCF is $3\times x^4=3x^4$.

Step4: Factor GCF from $2+4x$

GCF is 2. Divide each term by 2: $\frac{2}{2}+\frac{4x}{2}=1+2x$.
Expression: $2(1+2x)$

Step5: Factor GCF from $15x+5x^2$

GCF is $5x$. Divide each term by $5x$: $\frac{15x}{5x}+\frac{5x^2}{5x}=3+x$.
Expression: $5x(3+x)$

Step6: Factor GCF from $6n^5+10n$

GCF is $2n$. Divide each term by $2n$: $\frac{6n^5}{2n}+\frac{10n}{2n}=3n^4+5$.
Expression: $2n(3n^4+5)$

Step7: Factor GCF from $8x^3+4$

GCF is 4. Divide each term by 4: $\frac{8x^3}{4}+\frac{4}{4}=2x^3+1$.
Expression: $4(2x^3+1)$

Step8: Factor GCF from $7y^5+7y^3$

GCF is $7y^3$. Divide each term by $7y^3$: $\frac{7y^5}{7y^3}+\frac{7y^3}{7y^3}=y^2+1$.
Expression: $7y^3(y^2+1)$

Step9: Factor GCF from $12x^4+18x^2$

GCF is $6x^2$. Divide each term by $6x^2$: $\frac{12x^4}{6x^2}+\frac{18x^2}{6x^2}=2x^2+3$.
Expression: $6x^2(2x^2+3)$

Answer:

1. $2$
2. $10x$
3. $3x^4$
4. $2(1+2x)$
5. $5x(3+x)$
6. $2n(3n^4+5)$
7. $4(2x^3+1)$
8. $7y^3(y^2+1)$
9. $6x^2(2x^2+3)$