Polynomial Algebra I

Polynomial Functions

Reteach on Algebra 2 Topic 3

Polynomial Functions

When you add and subtract polynomial expressions you can only add like terms.
Example:

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

 $2x^2+3x^2+3x-5x-3+6$  
 $5x^2-2x+3$  

Polynomial Functions

 When you multiply polynomial expressions, you distributed every term in one parenthesis to every term in the second parenthesis.
Example:

 $\left(2x^2-5x+4\right)\left(x-3\right)$  
 $2x^2\left(x\right)+2x^2\left(-3\right)-5x\left(x\right)-5x\left(-3\right)+4\left(x\right)+4\left(-3\right)$   $2x^3-6x^2-5x^2+15x+4x-12$  
 $2x^3-11x^2+19x-12$  

Multiple Choice

Simplify  $$\left(3x^3-2x^{2\ }-\ 7\right)+\left(2x^2+6x\ -3\right)$$  

• $$3x^3+4x^2+6x\ -10$$  

• $$5x^3+4x^2-10$$  

• $$3x^3+6x-10$$  

• $$3x^3+6x+10$$  

Multiple Choice

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

Simplify

• $$5x^3-18x^2-11x+12$$  

• $$5x^3+18x^2+11x+12$$  

• $$5x^2-18x^2-11x-12$$  

• $$5x^3-18x+11x+12$$  

Zeros of a Polynomial Function

When we are looking to solve a polynomial function, often times we are looking for the x-value that makes the whole function equal to zero.

Zeros of a Polynomial Function

Find the zeros of the following function:

 $f\left(x\right)=3x^3-9x^2-12x$  

 $Factor\ f\left(x\right)=3x\left(x^2-3x-4\right)$  
 $Factor\ trinomial\ f\left(x\right)\ =\left(3x\right)\left(x-4\right)\left(x+1\right)$   $The\ zreos\ of\ the\ function\ are\ x=0,\ x=4,\ x=-1$  

Multiple Choice

$$f\left(x\right)=x^3-8x^2+16x$$  

Find the zeros of the following function:

• $$x=0,\ x=4,\ x=-4$$  

• $$x=0,\ x=4$$  

• $$x=0,\ x=-4$$  

• $$x=0,\ x=8,\ x=-16$$