Question

find the greatest common factor of the expressions
$33y^3x^4$
$3y^3x^6$
$9y^4x^3$
show your work here
hint: to add an exponent ($x^n$), type \exponent\ or press \^\
$\circ\\ 3y^{-3}x^{-3}$ $\circ\\ 3y^{-3}x^3$
$\circ\\ 6y^3x^3$ $\circ\\ 3y^3x^3$

factor the expression.
$11m^4 + 19m$
show your work here
hint: to add an exponent ($x^n$), type \exponent\ or press \^\

Explanation:

Step1: Find GCF of coefficients

Coefficients: 33, 3, 9. Prime factors: $33=3\times11$, $3=3$, $9=3^2$. GCF is 3.

Step2: Find GCF of $x$-terms

$x$-terms: $x^4$, $x^6$, $x^3$. GCF uses lowest exponent: $x^3$.

Step3: Find GCF of $y$-terms

$y$-terms: $y^3$, $y^3$, $y^4$. GCF uses lowest exponent: $y^3$.

Step4: Combine GCF components

Multiply coefficient, $x$-term, $y$-term GCFs: $3 \times y^3 \times x^3$

Step5: Factor $11m^4+19m$

Identify GCF of terms: $m$. Factor out $m$: $m(11m^3 + 19)$

Answer:

1. D. $3y^3x^3$
2. $m(11m^3 + 19)$