Question

no additional details were added for this assignmen
view submission
factoring day 1
score: 28/48 answered: 14/24
question 15
factor the gcf out of the polynomial below:
$12x^6 + 28x^4 + 20x^3$
question help: video

Explanation:

Step1: Find GCF of coefficients

The coefficients are 12, 28, 20.
Factors of 12: $1,2,3,4,6,12$
Factors of 28: $1,2,4,7,14,28$
Factors of 20: $1,2,4,5,10,20$
Greatest common factor is $4$.

Step2: Find GCF of variable terms

The variable terms are $x^6, x^4, x^3$.
The lowest exponent of $x$ is $3$, so GCF is $x^3$.

Step3: Combine GCFs

Multiply the coefficient GCF and variable GCF: $4 \times x^3 = 4x^3$.

Step4: Divide each term by GCF

$\frac{12x^6}{4x^3} = 3x^3$, $\frac{28x^4}{4x^3} = 7x$, $\frac{20x^3}{4x^3} = 5$

Step5: Write factored form

Place GCF outside parentheses, quotient terms inside.
$4x^3(3x^3 + 7x + 5)$

Answer:

$4x^3(3x^3 + 7x + 5)$