Factoring Expressions 3.4

Factoring Expressions 3.4

Using GCF, rational numbers (pos/neg; fraction/decimal/whole), and coefficients

Factoring using GCF (divide all terms by)

• make a list of common factors or use prime factorization

• select the largest factor they have in common

• For example:

•  $25d+30$  

•  $25d:\ 1,\ 5,\ 25,\ d$  

•  $30:\ 1,\ 2,\ 3,\ 5,\ 6,\ 10,\ 15,\ 30$  

• Highest common factor is 5

Multiple Select

Factor using GCF (check all that apply)

 $16p-8$  

•  $4\left(4p-2\right)$  

•  $4\left(-2+4p\right)$  

•  $8\left(2p-1\right)$  

•  $8\left(-1+2p\right)$  

•  $2\left(8p-4\right)$  

Multiple Select

Factor using GCF (Check all that apply)

 $8-22a$  

•  $4\left(2-6a\right)$  

•  $2\left(4-11a\right)$  

•  $8\left(1-3a\right)$  

•  $2\left(4+-11a\right)$  

•  $4\left(2+-6a\right)$  

Multiple Select

Factor using GCF (check all that apply)

 $32v+24w$  

•  $4\left(8v+6w\right)$  

•  $2\left(16v+12w\right)$  

•  $8\left(4v+3w\right)$  

•  $12\left(3v+2w\right)$  

Multiple Select

Factor using GCF (check all that apply)

 $12y-42z$  

•  $2\left(6y-21z\right)$  

•  $3\left(4y-14z\right)$  

•  $6\left(2y-7z\right)$  

•  $12\left(y-2z\right)$  

Multiple Choice

True or false?

Adding a negative is the same thing as subtracting a positive

• True

• False

Factor out the coefficient of the variable term

• identify which term is the variable term (has a letter)

• the coefficient is the number in front of the letter

• divide each term by the coefficient

• if you are "dividing by a fraction" remember to use the multiplicative inverse (change division to multiplication and flip the second fraction)

Multiple Choice

Which term is the variable term?

 $\frac{1}{2}m+\frac{1}{2}$  

•  $\frac{1}{2}m$  

•  $\frac{1}{2}$  

Multiple Choice

Which shows correct way to factor out the fraction?

•  $\frac{1}{2}m\times\frac{1}{2}$  

•  $\frac{1}{2}m\times\frac{2}{1}$  

Multiple Choice

Which expression is correct when we factor out the coefficient of the variable term?

 $\frac{1}{2}m+\frac{1}{2}$  

•  $\frac{1}{2}\left(\frac{1}{4}m+\frac{1}{4}\right)$  

•  $\frac{1}{2}\left(1m+1\right)$  

•  $\frac{1}{2}\left(m+1\right)$  

Multiple Select

Factor out the coefficient of the variable term (check all that apply)

 $\frac{2}{3}j-\frac{2}{9}$  

•  $\frac{2}{3}\left(j-\frac{1}{3}\right)$  

•  $\frac{2}{3}\left(1j-\frac{1}{3}\right)$  

•  $\frac{2}{3}\left(\frac{4}{9}j-\frac{4}{27}\right)$  

•  $\frac{2}{3}\left(j+-\frac{1}{3}\right)$  

•  $\frac{2}{3}\left(\frac{4}{9}j+-\frac{4}{27}\right)$  

Multiple Select

Factor out the coefficient of the variable term (check all that apply)

 $1.5a-4.5$  

•  $1.5\left(1a-3\right)$  

•  $1.5\left(1a+-3\right)$  

•  $1.5\left(a-3\right)$  

•  $1.5\left(a+-3\right)$  

Multiple Select

Factor out the coefficient of the variable term (check all that apply)

 $\frac{3}{10}x-\frac{3}{5}$  

•  $\frac{3}{10}\left(x+-2\right)$  

•  $\frac{3}{10}\left(x-2\right)$  

•  $\frac{3}{10}\left(\frac{9}{100}x-\frac{9}{50}\right)$  

•  $\frac{3}{10}\left(\frac{9}{100}x+-\frac{9}{50}\right)$  

Multiple Select

 $Factor\ out\ -\frac{1}{6}out\ of\ -\frac{1}{3}x+\frac{5}{6}y$  

•  $-\frac{1}{6}\left(2x+-5y\right)$  

•  $-\frac{1}{6}\left(2x-5y\right)$  

•  $-\frac{1}{6}\left(\frac{1}{18}x+-\frac{5}{36}y\right)$  

•  $-\frac{1}{6}\left(\frac{1}{18}x-\frac{5}{36}y\right)$