Question

An expression is shown below: 3pf2 − 21p2f + 6pf − 42p2 Part A: Rewrite the expression by factoring out the greatest common factor. (4 points) Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

Answer 1

$\huge\underline\bold\red{AnswEr}$

3pf² - 21p²f + 6pf - 42p²

= 3pf² + 6pf - 21p²f - 42p²

= 3pf(f +2) - 21p²(f + 2)

= (3pf - 21p²)(f +0 2)

Answer: (3pf - 21p²)(f + 2)

Answer 2

A.) (3pf -21$p^{2}$) (f+02) and B.) (3pf - 21$p^{2}$) (f+02)

Given:

3pf2 − 21p2f + 6pf − 42p2 to rewrite them in the expression by factoring out the greatest common factor

To Find:

The greatest common factor from the entire expression

Solution:

Expressing the greatest factor,

= 3p$f^{2}$+6pf-21$p^{2}$f-42 $p^{2}$

= 3pf(f+2) - 21 $p^{2}$(f+2)

= (3pf -21$p^{2}$)(f+02)

Factor to give the entire expression completely,

= 3p$f^{2}$ +6pf -21 $p^{2}$f - 42$p^{2}$

= 3pf(f+2) -21$p^{2}$(f+2)

=(3pf - 21$p^{2}$)(F+02)

Hence, the factored GCF : (3pf -21$p^{2}$) (f+2)

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