Respuesta :
Given:
The expression is:
[tex]3pf^2-21p^2f+6pf-42p^2[/tex]
To find:
The factored form of the given expression by taking out the GCF.
Solution:
We have,
[tex]3pf^2-21p^2f+6pf-42p^2[/tex]
In the given expression the terms are [tex]3pf^2,-21p^2f,6pf,-42p^2[/tex]. The common factors are [tex]3,p[/tex].
[tex]GCF=3\times p[/tex]
[tex]GCF=3p[/tex]
Taking out the GCF from the given expression, we get
[tex]=3p(f^2-7pf+2f-14p)[/tex]
After the complete factor, we get
[tex]=3p(f(f-7p)+2(f-7p))[/tex]
[tex]=3p(f-7p)(f+2)[/tex]
Therefore, the factored form after taking out the GCF is [tex]3p(f^2-7pf+2f-14p)[/tex] and the complete factored form is [tex]3p(f-7p)(f+2)[/tex].
