Review: 5 Types of Factoring

Review: 5 Types of Factoring

In this Quizizz Lesson, we'll review the five types of factoring we have discussed in class so far.

Greatest Common Factor (GCF)

The highest expression that divides completely into two or more terms.

It is the largest factor that a set of expressions has in common.

Multiple Choice

Which of the following is the factored form of the given expression?

 $15m^3n+20mn^2-10m^2n$  

•  $5\left(m^3n+4mn^2-2m^2n\right)$  

•  $m^3n^3\left(15+20-10\right)$  

•  $5mn$  

•  $3m^2+4n-2m$  

•  $5mn\left(3m^24n-2m\right)$  

Factoring Trinomials (a = 1)

Always factor out the GCF first!

When in standard form, your trinomial will look like

 $ax^2+bx+c$  

Find two factors of "c" that add to "b."

Multiple Choice

Factor the given expression.

 $4x^2-4x-48$  

• 4(x+12)(x-1)

• 2(x+3)(x-4)

• 4(x+6)(x-2)

• 4(x+4)(x-3)

• 4(x+3)(x-4)

Difference of Squares

Remember: this ONLY works if you have SUBTRACTION.

Multiple Choice

Factor the given expression.

 $4x^2-100$  

• 2(x+5)(x-5)

• 2(x-5)(x-5)

• (2x-10)(2x+10)

• Nice try, but this one can't be factored!

Sum of Cubes

Difference of Cubes

Follow the pattern to fill in the "blank spots."

For the signs, remember the word SOAP (Same - Opposite - Always Positive)

Multiple Choice

Factor the given expression.

 $16n^3-2$  

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

•  $2\left(n-1\right)\left(n^2+n+1\right)$ 

•  $\left(2n-2\right)\left(4n^2+4n+4\right)$ 

•  $2\left(n+1\right)\left(n^2-n+1\right)$  

Perfect Square Trinomials

Multiple Choice

Factor the given expression.

 $16x^2-48x+36$  

•  $\left(4x+6\right)^2$  

•  $\left(4x-6\right)^2$  

•  $4\left(2x+3\right)^2$  

•  $4\left(2x-3\right)^2$  

Mixed Review!

The rest of the questions aren't separated by type. You will have to identify the correct type of factoring and then do it!

Multiple Choice

Which method of factoring would you use for this expression?

 $9x^2-4$  

• Greatest Common Factor

• Trinomial with a=1

• Difference of Squares

• Sum/Difference of Cubes

• Perfect Square Trinomial

Multiple Choice

Which method of factoring would you use for this expression?

 $x^2+8x+12$  

• Greatest Common Factor

• Trinomial with a=1

• Difference of Squares

• Sum/Difference of Cubes

• Perfect Square Trinomial

Multiple Choice

Which method of factoring would you use for this expression?

 $4x^2y^2+24abxy+36a^2b^2$  

• Greatest Common Factor

• Trinomial with a=1

• Difference of Squares

• Sum/Difference of Cubes

• Perfect Square Trinomial

Multiple Choice

Which method of factoring would you use for this expression?

 $16c^2+36$  

• Greatest Common Factor

• Trinomial with a=1

• Difference of Squares

• Sum/Difference of Cubes

• Perfect Square Trinomial

Multiple Choice

Which method of factoring would you use for this expression?

 $c^3-8d^3$  

• Greatest Common Factor

• Trinomial with a=1

• Difference of Squares

• Sum/Difference of Cubes

• Perfect Square Trinomial

Last Section!

You're completely on your own... :)

Multiple Choice

Factor the expression.

 $7x^3+14x^2+7x$  

• 7x(x+1)^2

• 7x(x^2+2x+1)

• 7(x^3+2x^2+x)

• x(7x^2+14x+7)