Factoring

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Practice of Factoring Expressions

A 7th Grade Review:
- GCF
- Trinomial to Two Binomials when a = 1
- DOTS

​GCF Factoring

Multiple Choice

Can you factor this expression with a GCF?

$$12x^3+3x^2$$  

• Yes

• No

Multiple Choice

Which of the following do you think is the GCF of

$$12x^3+3x^2$$  

• $$3x$$  

• 3

• $$3x^2$$  

• $$3x^3$$  

Multiple Choice

Which of the following is the factored form of:

$$12x^3+3x^2$$  

• $$3x\left(4x^2-x\right)$$  

• $$3\left(4x^3-x^2\right)$$  

• $$3x^2\left(4x+1\right)$$  

• $$3x^3\left(4x+1\right)$$  

Multiple Choice

Can you factor this expression with a GCF?

$$10x^2+2x-\ 5$$  

• Yes

• No

Trinomial to Two Binomials when a = 1

Multiple Choice

Can you factor this expression with the method of trinomial into two binomials?

$$x^2-16$$  

• Yes

• No

Multiple Choice

Can you factor this expression with the method of trinomial into two binomials?

$$x^2+10x\ +16$$  

• Yes

• No

Multiple Choice

Which pair of numbers is not a factor pair of the c term?

$$x^2+10x\ +16$$  

• 1 and 16

• 4 and 4

• 2 and 8

• 6 and 10

Multiple Choice

What is the factored form of the given expression?

$$x^2+10x\ +16$$  

• (x + 1)(x + 16)

• (x + 4)(x + 4)

• (x + 6)(x + 10)

• (x + 2)(x + 8)

DOTS - Difference of Two Squares

Multiple Choice

Can you factor this expression with the method of DOTS?

$$x^2-16$$  

• Yes

• No

Multiple Choice

What is the factored form of the expression?

$$x^2-16$$  

• (x + 4)(x - 4)

• (x + 4)(x + 4)

• (x - 4)(x - 4)

Multiple Choice

Can you factor this expression with the method of DOTS?

$$x^2+100$$  

• Yes

• No

Time to practice
identifying factoring methods
for expressions!

Multiple Choice

What type of factoring should be done for this expression?

$$16x^2-9$$  

• Greatest Common Factor

• Difference of Squares

• Trinomial to Two Binomials

Multiple Choice

What type of factoring should be done for this expression?

$$15x^2-5x$$  

• Greatest Common Factor

• Difference of Squares

• Trinomial to Two Binomials

Multiple Choice

What type of factoring should be done for this expression?

$$8x^2-4x+10$$  

• Greatest Common Factor

• Difference of Squares

• Trinomial to Two Binomials

Multiple Choice

What type of factoring should be done for this expression?

$$x^2-4x-45$$  

• Greatest Common Factor

• Difference of Squares

• Trinomial to Two Binomials

Multiple Choice

What type of factoring should be done for this expression?

$$x^2+16x+55$$  

• Greatest Common Factor

• Difference of Squares

• Trinomial to Two Binomials

Multiple Choice

What type of factoring should be done for this expression?

$$36x^2-y^2$$  

• Greatest Common Factor

• Difference of Squares

• Trinomial to Two Binomials

Time to practice
factoring expressions!

Multiple Choice

Factor x² - 121

• (x - 11)(x - 11)

• (x + 11)(x + 11)

• (x + 11)(x - 11)

• (x - 9)(x + 9)

Multiple Choice

Factor
x² - 9x + 20

• (x - 10)(x - 2)
• (x - 20)(x - 1)
• (x - 10)(x + 2)
• (x - 5)(x - 4)

Multiple Choice

Factor
k² - 2k - 24

• (k+4)(k-6)
• (k+4)(k+6)
• (k+6)(k-1)
• (k-4)(k+6)

Multiple Choice

Factor 81m² - 4

• (2m - 9)(2m + 9)

• (9m - 2)(9m - 2)

• (m - 2)(m + 9)

• (9m - 2)(9m + 2)

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
a² - a - 12

• (a - 4)(a + 3)
• (a + 6)(a - 4)
• (a - 6)(a + 4)
• (a + 4)(a - 3)

Multiple Choice

Factor the polynomial.

    $$5x^4-40x^3+10x^2$$  

•      $$5x^2\left(5x^4-8x^3+2x^2\right)$$  

•      $$5\left(x^4-8x^3+2x^2\right)$$  

•      $$5x^4\left(1-8x^2+2x\right)$$  

•      $$5x^2\left(x^2-8x+2\right)$$  

Multiple Choice

Factor the polynomial.

$$12x^5+16x^3$$   

•   $$4x^3\left(3x^5+4x\right)$$  

•   $$2x^3\left(6x^2+8\right)$$  

•   $$4x^3\left(3x^2+4\right)$$  

•   $$6x\left(2x^4+3x^2\right)$$  

Multiple Choice

Factor the polynomial.

  $$6x^2-9x+9$$  

•    $$3x\left(2x-3x+3\right)$$  

•    $$3\left(2x^2+3x+3\right)$$  

•    $$3x\left(3x^2-6x+6\right)$$  

•    $$3\left(2x^2-3x+3\right)$$  

Multiple Choice

Factor k² + 36

• (k - 6)(k + 6)

• (k + 6)(k +6)

• (k - 6)(k - 6)

• Not factorable

Multiple Choice

Factor the polynomial.

      $$36x^7+12x^5+28x^4$$  

•        $$2x^4\left(18x^3+6x+14\right)$$  

•        $$4x^4\left(9x^3+3x+7\right)$$  

•        $$4x\left(9x^3+3x+7\right)$$  

•        $$4x^3\left(9x+3x+7\right)$$  

Multiple Choice

Factor
x² + 5x + 4

• (x + 4)(x + 1)
• (x + 2)(x + 2)
• (x + 4)(x - 1)
• (x + 5)(x + 1)

Multiple Choice

Factor 9x² - 64

• (3x - 8)(3x + 8)

• (3x + 8)²

• (3x - 8)²

• (x + 8)(x - 8)

Multiple Choice

Factor the polynomial.

   $$50x^3+60x^2-60$$  

•     $$5\left(10x^3+12x^2-12\right)$$  

•     $$10\left(5x^3+6x^2-6\right)$$  

•     $$10x\left(5x^3+6x^2-6\right)$$  

•     $$10x\left(5x^2+6x-6\right)$$  

Poll

How would you rate your confidence with this topic of factoring?

• I still need a lot of help

• I think I will be okay if I study a bit more

• I will be ready for the upcoming quiz

• I love factoring, bring it on!