Fall Break Review - Factoring and Completing the Square

Fall Break Review - Factoring and Completing the Square

by Tracey Stark

​Factoring: The first step is ...

Multiple Choice

Factor completely:    $$7x^3-49x^2+21x$$  

• $$7\left(x^3-7x^2+3x\right)$$  

• $$7x\left(x^2-7x+3\right)$$

• $$x\left(7x^2-49x^2+21x\right)$$  

• $$7x^3\left(-7x+3\right)$$

Multiple Choice

Factor completely: $$5x^3+10x^2-75x$$  

• $$5x\left(x^2+2x-15\right)$$  

• $$5\left(x^3+2x^2-15x\right)$$  

• $$5x\left(x+5\right)\left(x-3\right)$$  

• $$x\left(5x^2+10x-75\right)$$  

​Factoring Special Case: Difference of Two Squares

Multiple Choice

Factor completely: $$3x^2-27$$  

• $$3\left(x-3\right)\left(x+3\right)$$  

• $$3\left(x^2-9\right)$$  

• not factorable

• $$\left(3x-3\right)\left(3x+3\right)$$  

​Factor when a = 1: What numbers multiply to be "c" but add to "b"

Multiple Choice

Factor completely:  $$6x^2+43x+55$$  

• $$\left(3x+11\right)\left(2x+5\right)$$  

• (2x-11)(3x-5)

• (2x+11)(3x+5)

• $$\left(3x-5\right)\left(4x+1\right)$$  

Multiple Choice

Factor completely: $$12x^2+4x-5$$  

• $$\left(2x-1\right)\left(6x+5\right)$$  

• $$\left(2x+1\right)\left(6x-5\right)$$  

• $$\left(3x+5\right)\left(4x-1\right)$$  

• $$\left(3x-5\right)\left(4x+1\right)$$  

Multiple Choice

Factor completely:  $$36x^2-114x-56$$  

• $$2\left(9x-4\right)\left(2x+7\right)$$  

• $$2\left(9x+4\right)\left(2x-7\right)$$  

• $$2\left(9x-7\right)\left(2x+4\right)$$  

• $$2\left(9x+7\right)\left(2x-4\right)$$  

​Completing the Square: Puts standard form of a quadratic equation into vertex form

​Complete the square example:

Multiple Choice

What is the vertex of $$\left(x-5\right)^2+46$$  ?

• $$\left(-5,\ 46\right)$$  

• $$\left(5,-46\right)$$  

• $$\left(x,\ 46\right)$$  

• $$\left(5,\ 46\right)$$  

Multiple Choice

Convert to vertex form:   $$g\left(x\right)\ =\ -5x^2+40x+17$$  

• $$g\left(x\right)=-5\left(x-4\right)^2-63$$  

• $$g\left(x\right)=-5\left(x+4\right)^2+97$$  

• $$g\left(x\right)=-5\left(x-4\right)^2+97$$  

• $$g\left(x\right)=-5\left(x-4\right)^2+63$$