Question

use the drop - down menus to complete the statements about factoring (14x^{2}+6x - 7x - 3) by grouping. the gcf of the group ((14x^{2}-7x)) is (square). the gcf of the group ((6x - 3)) is (square). the common binomial factor is (square). the factored expression is (square).

Explanation:

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

Identify shared factors: $14x^2=7x \cdot 2x$, $7x=7x \cdot 1$. GCF is $7x$.

Step2: Find GCF of $6x-3$

Identify shared factors: $6x=3 \cdot 2x$, $3=3 \cdot 1$. GCF is $3$.

Step3: Factor out GCFs from groups

$14x^2-7x = 7x(2x-1)$; $6x-3 = 3(2x-1)$.

Step4: Identify common binomial factor

From factored groups, common binomial is $2x-1$.

Step5: Write fully factored expression

Combine factors: $(7x+3)(2x-1)$.

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 $(7x+3)(2x-1)$