Unit 2 Review

Unit 2 Review

Rationals

Simplifying Rationals

•  $\frac{9y^7}{24y^2}$  

• Factor out the GCF

Multiple Choice

Simplify

 $\frac{12n^3}{18n^5}$  

•  $\frac{12n^{ }}{18n^2}$  

•  $\frac{2n^3}{3n^5}$  

•  $\frac{2}{3n^2}$  

•  $\frac{4n^{ }}{6n^2}$  

Multiple Choice

Simplify  $\frac{21m^8}{14m^3}$  

•  $\frac{3m^5}{2}$  

•  $\frac{21m^5}{14}$  

•  $\frac{3m^8}{2m^3}$  

•  $\frac{7m^5}{3}$  

Perfect Square Trinomials (Polynomials)

• First and Last Terms - Look for perfect squares (coefficients and variables)

• Middle Term - Look for the 2 times the roots of the perfect squares

•  $x^2+2xy+y^2$  

•  $\left(x+y\right)^2=\left(x+y\right)\left(x+y\right)$  

Multiple Select

Select all the polynomials that are perfect squares.

• $4x^2+12x+9$

• $25x^2+20xy+4y^2$

• $3x^2+6x+y^2$

• $49x^2+84xy+36y^2$

Multiple Select

Select all the polynomials that are perfect squares.

•  $2x^2+4y+2$ 

•  $x^2+2xy+y^2$ 

•  $4x^2+12xy+9y^2$ 

•  $4x^2+12x+9y^2$ 

Difference of Squares Polynomials

• Look for the subtraction of a perfect square from another.

• There will be no middle term.

•  $x^2-y^2$  

•  $\left(x+y\right)\left(x-y\right)$  

Multiple Select

Which polynomials are a difference of squares?

• $4x^2+12x+9$

•  $25x^2-4y^2$ 

•  $x^2-9y^2$ 

• $49x^2+84xy+36y^2$

Multiple Choice

For  $2x^2+9x+4$ ,  $a\ne1$  .

• True

• False

Multiple Choice

Since  $a\ne1$ , find the factors of a*c that add to b, and rewrite as 

•  $\left(ax^2+b_1x\right)+\left(b_2x+c\right)$  

•  $\left(x+b_1\right)\left(x+b_2\right)$  

Multiple Choice

Factor

 $2x^2+9x+4$  

• (x+4)(2x+1)

• (x-4)(2x+1)
  

• (2x+3)(x+2)

• Unfactorable
  

Multiple Choice

For  $x^2-x-12$ ,  $a\ne1$  .

• True

• False

Multiple Choice

Since  $a=1$ , find the factors of c that add to b, and rewrite as

•  $\left(ax^2+b_1x\right)+\left(b_2x+c\right)$  

•  $\left(x+b_1\right)\left(x+b_2\right)$  

Multiple Choice

Factor  $x^2-x-12$  

• (x+4)(x-3)
  

• (x-4)(x+3)

• (x-6)(x+2)

• Unfactorable

To solve rational equations, what's an important step?

 $\frac{2}{x+3}=\frac{5}{x+4}$  

Multiple Choice

Solve   $\frac{x+4}{2}=\frac{2x+1}{3}$  

• x=3

• x=6

• x=10

• x=12

Multiple Choice

Solve    $\frac{x+2}{x^2+7x+10}=1$  

•  $x=-4$  

•  $x=0$  

•  $x=2$  

•  $x=7$