Question

question 4 (4 points) to completely factor (6c^{7}d^{4}+24c^{5}d^{3}-18c^{3}d^{2}), what is the greatest common factor that will be taken out first?

Explanation:

Step1: Find GCF of coefficients

The coefficients are 6, 24, -18.
Factors of 6: 1,2,3,6
Factors of 24: 1,2,3,4,6,8,12,24
Factors of 18: 1,2,3,6,9,18
Greatest common factor (GCF) = 6

Step2: Find GCF of $c$-terms

The $c$-terms are $c^7$, $c^5$, $c^3$.
Use the lowest exponent: $c^3$

Step3: Find GCF of $d$-terms

The $d$-terms are $d^4$, $d^3$, $d^2$.
Use the lowest exponent: $d^2$

Step4: Combine all GCFs

Multiply the GCF of coefficients, $c$-terms, and $d$-terms.
$\text{GCF} = 6 \times c^3 \times d^2 = 6c^3d^2$

Answer:

$6c^3d^2$