Algebra 2 End of Quarter Test (Second Term)

The polynomial $4x^2y^3-2x^3y^2-x^3y+7xy^3$   square feet models the area of Building 1. The polynomial  $-6x^3y^2-xy^3+2x^3y-5x^3y^3$  square feet models the area of Building 2. Write a polynomial that expresses the difference in areas between Building 1 and Building 2.

•  $5x^3y^3+4x^3y^2-2x^3y+4x^2y^3-8xy^3$  

•  $5x^3y^3-8x^3y^2+x^3y-6xy^3+4x^2y^3$  

•  $5x^3y^3+4x^3y^2-3x^3y+4x^2y^3+8xy^3$  

•  $5x^3y^3+4x^3y^2+3x^3y+4x^2y^3+8xy^3$  

Simplify the expression.

 $\left(4x+7y\right)\left(3x^2y-2xy+5y^2\right)$  

•  $12x^3y-8x^2y+6xy^2+21x^2y^2+35y^3$  

•  $12x^3y-8x^3y^2+6xy^2+21x^2y^2+35y^3$  

•  $12x^3y+8x^2y-6xy^2-21x^2y^2-35y^3$  

•  $12x^3y+8xy^2+6x^2y+21x^2y^2+35y^3$  

 Rewrite the expression by factoring out the GCF (greatest common factor).

 $5x^2\left(z+6\right)-7y^3\left(z+6\right)$ 

Factor the expression completely.

 $72x^4y^2+18x^3y^2-200x^2y^2-50xy^2$ 

Simplify the expression:  $\frac{6-5i}{3+4i}$  

Solve the equation using the quadratic formula:

 $4x^2+2x-7=-x^2+13x-9$  

Quadratic formula:
 $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$  

Given $f\left(x\right)=\ 3x^2-2x+1$   and  $g\left(x\right)=4x-5$  ,

find  $\left(f-g\right)\left(x\right)$  .

Given $f\left(x\right)=\ 3x^2-2x+1$   and  $g\left(x\right)=4x-5$  ,

find  $\left(gf\right)\left(x\right)$  .

•  $-12x^3+23x^2-14x-5$  

•  $-12x^3-23x^2-14x+5$   

•  $12x^2-8x-1$   

•  $12x^2-8x-1$   

•  $-12x^3-23x^2+14x-5$  

Given $f\left(x\right)=\ 3x^2-2x+1$   and  $g\left(x\right)=4x-5$  ,

find  $g\left(f\left(x\right)\right)$  .

Given $f\left(x\right)=\ 3x^2-2x+1$   and  $g\left(x\right)=4x-5$  ,

find  $\left(f\circ\ g\right)_{\left(-1\right)}$  .