Question

factoring by gcf & grouping worksheet

1. $2x^4 + 8x$
2. $12p^3 - 21p^2 + 28p - 49$

Explanation:

Step1: Find GCF of $2x^4+8x$

Identify GCF of coefficients ($2,8$) is $2$, GCF of variables ($x^4,x$) is $x$. Total GCF: $2x$.

Step2: Factor out GCF from $2x^4+8x$

$\frac{2x^4+8x}{2x} = x^3 + 4$, so $2x(x^3 + 4)$

Step3: Group terms for $12p^3-21p^2+28p-49$

Group into $(12p^3-21p^2)+(28p-49)$

Step4: Factor GCF from each group

First group GCF: $3p^2$, so $3p^2(4p-7)$; Second group GCF: $7$, so $7(4p-7)$

Step5: Factor out common binomial

Common binomial: $(4p-7)$, so $(3p^2+7)(4p-7)$

Answer:

1. $2x(x^3 + 4)$
2. $(3p^2 + 7)(4p - 7)$