Algebra 2 -- Add, Subtract, Multiply, Divide Polynomials

Simplify the following expression:

 $\frac{1}{4}\left(12x\ -\ 8y\right)\ -\ 11\left(3x\ +\ 2y\ -\ 5\right)$  

•  $-36x\ -\ 20y\ -\ 55$  

•  $-30x\ -\ 24y\ +\ 55$  

•  $-30x\ +\ 4y\ +\ 55$  

•  $-27x\ +\ 20y\ -\ 55$  

Tags

CCSS.6.EE.A.3

Simplify the following expression:

 $\left(4x^2\ -\ 10\right)\left(8x\ -\ 100\right)$  

•  $12x^3\ -\ 110$  

•  $32x^2\ -\ 400x\ -\ 80$  

•  $32x^3\ -\ 400x^2\ -\ 80x\ +\ 1000$  

•  $12x^3\ -\ 400x^2\ -\ 2x\ -\ 1000$  

Tags

CCSS.HSA.APR.A.1

Find the quotient and remainder after dividing using long division.

 $\left(x^4\ +\ 3x^3\ +\ 2x\ +\ 1\right)\div\left(x^2\ +\ x\ +\ 1\right)$  

•  $x^2\ +\ 2x\ -\ 3\ +\ \frac{3x\ +\ 4}{x^2\ +\ x\ +\ 1}$  

•  $x^2\ +\ 2x\ -\ \frac{x^2\ -\ x}{x^2\ +\ x\ +\ 1}$  

•  $x^2\ +\ 4x\ +\ 5\ +\ \frac{11x\ +\ 6}{x^2\ +\ x\ +\ 1}$  

•  $x^2\ +\ 4x\ -\ 3\ +\ \frac{2x\ +\ 1}{x^2\ +\ x\ +\ 1}$  

Tags

CCSS.HSA.APR.D.6

Find the quotient and remainder after dividing using synthetic division.

 $\left(4x^3\ +\ 3x^2\ +\ 2x\ +\ 4\right)\div\left(x\ +\ 2\right)$  

•  $4x^2\ +\ 11x\ +\ 24\ +\ \frac{52}{x\ +\ 2}$  

•  $4x^2\ +\ 11x\ -\ 20\ +\ \frac{44}{x\ +\ 2}$  

•  $4x^2\ +\ 5x\ +\ 8\ +\ \frac{20}{x\ +\ 2}$  

•  $4x^2\ -\ 5x\ +\ 12\ -\ \frac{20}{x\ +\ 2}$  

Tags

CCSS.HSA.APR.D.6

The polynomial

 $6x^3\ -\ 33x^2\ +\ 49x\ -\ 12$   represents the volume in cubic meters of a rectangular gasoline holding tank at NASA in Houston, TX. The height of the tank is (x - 3). Use synthetic division to help you find the polynomial that represents the area of the base for the holding tank. (Hint: The volume of a rectangular solid is given by (Area of the base x Height)). 

•  $6x^2\ -\ 51x\ +\ 202\ -\ \frac{618}{x\ -\ 3}$  

•  $6x^2\ +\ 15x\ +\ 94\ +\ \frac{270}{x\ -\ 3}$  

•  $6x^2\ -\ 51x\ +\ 4$  

•  $6x^2\ -\ 15x\ +\ 4$  

Tags

CCSS.HSA.APR.D.6

Given

 $f\left(x\right)=x^2+6$  and  $g\left(x\right)=2x\ -\ 1$  , find  $f\left(g\left(x\right)\right)$  .

•  $x^2\ +\ 2x\ +\ 5$  

•  $2x^2\ +\ 11$  

•  $4x^2\ +\ 5$  

•  $4x^2\ -\ 4x\ +\ 7$  

Tags

CCSS.HSF-BF.A.1C

Given  $f\left(x\right)=x^2+6$  and  $g\left(x\right)=2x\ -\ 1$  , find  $g\left(f\left(x\right)\right)$  .

•  $4x^2\ -\ 4x\ +\ 7$  

•  $x^2\ +\ 2x\ +\ 5$  

•  $2x^2\ +\ 11$  

•  $4x^2\ +\ 5$  

Tags

CCSS.HSF-BF.A.1C