4.2 Factoring

Multiply the following, using the distributive property:

$\mathrm{3x}({\mathrm{4x}}^2+\mathrm{5x}+2)=$ ____________________

Now, you’re going to do the same thing backward .

• A

  “Pull out” the common term of $\mathrm{4y}$ from the following expression.

• $\text{16}{y}^3+\mathrm{4y}+\mathrm{8y}=\mathrm{4x}(\text{\_\_\_\_\_\_\_\_\_})$

• B

  Check yourself, by multiplying $\mathrm{4y}$ by the term you put in parentheses.

• C

  Did it work? _______________

$9\text{xy}+\text{12}x=$ ____________________

$\text{10}{x}^2+{\mathrm{9y}}^2=$ ____________________

$\text{100}{x}^3+\text{25}{x}^2=$ ____________________

${\mathrm{4x}}^{2}y+{\mathrm{3y}}^{2}x=$ ____________________

$x^2-9=$ ______________

$x^2-\text{10}x+\text{25}=$ ______________

$x^2+\mathrm{8x}+\text{16}=$ ______________

$x^2+9=$ ______________

${\mathrm{3x}}^2-\text{27}=$ ______________

• A

  $x^2+\mathrm{7x}+\text{10}=$ ______________

• B

  Check your answer by multiplying back:

• A

  $x^2-\mathrm{5x}+6=$ ______________

• B

  Check your answer by plugging a number into the original expression, and into your modified expression:

$x^2-\mathrm{6x}+5=$ ______________

$x^2+\mathrm{8x}+6=$ ______________

$x^2-x-\text{12}=$ ______________

$x^2+x-\text{12}=$ ______________

$x^2+\mathrm{4x}-\text{12}=$ ______________

${\mathrm{2x}}^2+\mathrm{7x}+\text{12}=$ ______________