Factor a monomial (the GCF) from each polynomial. $36x + 9$

Solutions

VerifiedThe greatest common factor (GCF) for the polynomial $36x+9$

$\begin{align*} & 36x+9\tag{Determine the GCF of all the polynomial terms}\\ & = 9(4x)+9(1)\tag{Writing each term as the product of the GCF and another factor}\\ & = 9(4x+1)\tag{Using the distributive property to factor out the GCF}\\ \end{align*}$

The greatest common factor (GCF) $=9$

Factor out the GCF from the polynomial.

$\begin{align*} 36x & = 4 \cdot \underline 9 \cdot x && {\text {factors of the first term}} \\ 9 & = 1 \cdot \underline 9 && {\text {factors of the second term}} \\ \text {GCF} & = 9 \\ \\ & = 9 \left (4x\right) + 9 \left (1\right) && {\text {product of the GCF and another factor}} \\ & = 9 \left (4x + 1\right) && {\text {distributive property to factor out the GCF}} \end{align*}$

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