use the drop - down menus to complete the statements about factoring 14x² + 6x - 7x - 3 by grouping. the gcf…

Explanation:

Step1: Find GCF of $14x^{2}-7x$

Factor out common terms. For $14x^{2}-7x$, we can factor out $7x$ since $14x^{2}=7x\times2x$ and $7x = 7x\times1$. So the GCF is $7x$.

Step2: Find GCF of $6x - 3$

Factor out common terms. For $6x-3$, we can factor out $3$ since $6x=3\times2x$ and $3 = 3\times1$. So the GCF is $3$.

Step3: Rewrite the original expression

$14x^{2}+6x - 7x-3=(14x^{2}-7x)+(6x - 3)=7x(2x - 1)+3(2x - 1)$.

Step4: Identify common binomial factor

The common binomial factor is $2x - 1$.

Step5: Write the factored - expression

Using the distributive property $ab+ac=a(b + c)$, where $a=(2x - 1)$, $b = 7x$ and $c = 3$, the factored expression is $(2x - 1)(7x+3)$.

Answer:

The GCF of the group $(14x^{2}-7x)$ is $7x$. The GCF of the group $(6x - 3)$ is $3$. The common binomial factor is $2x - 1$. The factored expression is $(2x - 1)(7x+3)$.