Factoring using GCF, Basic Factoring, & Difference of Two Squares

Multiplying Expressions

AND

Factoring using GCF, Basic Factoring, & Difference of Two Squares

​QUIZ REVIEW

Multiple Choice

The following polynomial is written in standard form: 7x³ - 11x² + 8x - 5

• True

• False

Multiple Select

Which of these is in Standard Form - Choose 2

• $$4+12x-13x^2$$

• $$5-3x$$  

• $$-12x^2+5x-9$$

• $$x^2-15$$

Multiple Choice

Simplify:

$$5\left(3x+2\right)$$  

• $$3x+10$$

• $$15x+10$$  

• $$15x-10$$  

• $$3x-10$$  

Multiple Choice

$$-3\left(2x-9\right)$$  

• $$-6x-9$$  

• $$6x-18$$  

• $$-6x-27$$  

• $$-6x+27$$  

Multiple Choice

$$\frac{1}{4}\left(8x-12\right)$$  

• $$\frac{1}{2}x-\frac{1}{3}$$  

• $$2x-3$$  

• $$4x-3$$  

• $$\frac{1}{2}x-\frac{2}{3}$$  

Multiple Choice

Find the product: (y - 3)(y + 7)

• y² - 21

• y² + 10y - 21

• y² + 4y - 21

• 2y - 10

Multiple Choice

(x + 5)²

• x² + 25

• x² + 10x + 25

• x² + 10 x + 10

• x² + 10

Multiple Choice

The length of a rectangle is x + 2 units and the width is 3x + 7

units. Find the area.

• 3x² + 9x + 14 square units

• 3x² + 13x + 14 square units

• 4x + 9 square units

• 8x + 18 square units

Fill in the Blank

What is the GCF of the following? 

$$6n^2+24n$$  

Fill in the Blank

What is the Greatest Common Factor of

$$9x^2+6$$  

Multiple Choice

Factor using the GCF:

$$2x^2+10x+42$$  

• $$2\left(x^2+5x+21\right)$$

• $$2\left(2x^2+10x+42\right)$$

• $$x^2+5x+21$$  

• $$2x\left(x^2+5x+21\right)$$  

​If you got it wrong and you said...

​Remember that when you take out the GCF, you need to divide each term by it!

​Remember that when you take out the GCF, you have to put it out in front!

​Remember you need to find a GCF that every term has in common... the term 21 does not have an x!

Multiple Choice

Factor x² - 13x + 36

•  (x + 9)(x + 4)

• (x - 9)(x - 4)

• (x + 9)(x - 4)

• (x - 9)(x + 4)

Multiple Choice

Factor n² + 16n + 63

• (n - 7)(n + 4)

• (n + 7)(n - 9)

• (n - 3)(n - 10)

• (n + 7)(n + 9)

Multiple Choice

Factor completely: 

Remember... GCF if there is one!!

3x² + 18x + 15

• 3(x² + 6x + 5)

• (x + 5)(x + 1)

• 3(x + 5)(x + 1)

• (x + 15)(x + 3)

PERFECT SQUARES

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Multiple Choice

Which expression can you factor by difference of squares?

• x² - 81

• x² + 81

• x² + 4x + 4

• x² - 24

Multiple Choice

Factor

$$4x^{2\ }-1$$  

• $$\left(2x+1\right)^2$$  

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

• $$\left(x+1\right)\left(x-1\right)$$  

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

Multiple Choice

Factor:

x² - 25

• ( x + 5 ) ( x - 5 ) 

• ( x - 5 ) ( x - 5 ) 

• ( x + 5 ) ( x + 5 ) 

• (x + 25)(x - 25)

Multiple Choice

Factor the following: $$36x^2-121$$  

• (6x + 11)(6x + 11)

• (6x - 11)(6x - 11)

• (6x + 11)²

• (6x + 11)(6x - 11)

Multiple Choice

4x² - 25

• (2x + 5) (2x - 5)

• (2x - 5)²

• (2x + 5)²

• (5x + 2)(5x - 2)

​Great Job!

For more practice, turn to page 22 in your packet!