Unit 4 and Polynomial Identities

What is an identity?

• When you set an equation equal to 0

• When you can reduce a fraction or an expression

• When the answer is no solution

• When the answer is infinite solutions

An identity is

• When the left side of the equation is the exact same as the right side equation

• When there is one solution

• When you plug in numbers and you get 0

• When the roots are real

Is

 $\left(x-y\right)^3=\left(x-y\right)\left(x+y\right)\left(x-y\right)$  an identity?

• yes

• no

 $\frac{x^4-y^4}{x^2-y^2}=x^2+y^2$  is an identity?

• True

• False

 $x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)$  is an identity?

• yes

• no

 $\frac{x^2+y^2}{x+y}=x+y$  is an identity?

• True

• False

 $\left(x+y+z\right)^2\$  is the same as

•  $2x^2+2y^2+2z^2$  

•  $x^2+y^2+z^2$  

•  $x^2+y^2+z^2+xy+xz+yz$  

•  $x^2+y^2+z^2+2xy+2xz+2yz$  

 $x^2+2x-24\$  can NOT be rewritten as 

•  $\left(x+6\right)\left(x-4\right)$  

•  $\left(x+1\right)^2-25$  

•  $\frac{x\left(x+6\right)\left(x^2-16\right)}{x^2+4x}$  

•  $x\left(x+6\right)+4\left(x-6\right)$  

 $\left(x+r\right)\left(x-q\right)\$  can not be rewritten as

•  $x^2+x\left(r-q\right)-qr$  

•  $x^2-qx+rx-rq$  

•  $x\left(x-q\right)+r\left(x-q\right)$  

•  $x^2-qr-rx+qx$  

Question is shown here

• I only

• I and II

• II and III

• I and III