Factoring General Trinomials

Factoring Trinomials

When we factor Trinomials, we are actually "undoing" FOIL.

In order to do that we look for the two numbers whose sum is the coefficient of the middle term, and whose product is the last the term.

Multiple Choice

• (x - 12)(x - 3)

• (x + 3)(x + 12)

• (x + 12)(x - 3)

• (x + 3)(x - 12)

Multiple Choice

• (x + 5)(x + 5)

• (x + 25)(x + 1)

• (x - 5)(x - 5)

• (x + 5)(x - 5)

Multiple Choice

• (x + 2)(x - 7)

• (x - 2)(x - 7)

• (x - 2)(x + 7)

• (x + 2)(x + 7)

Multiple Choice

Factor

x² -16x + 48

• (x - 12)(x - 4)

• (x + 6)(x - 8)

• (x + 12)(x - 4)

• (x -16)(x - 3)

Multiple Choice

• (x + 6)(x + 2)

• (x + 3)(x + 4)

• (x - 4)(x - 3)

• (x - 2)(x - 6)

Multiple Choice

Factor

x² - 9 x - 36

• (x - 12)(x + 3)

• (x + 9)(x - 4)

• (x + 12)(x - 3)

• (x - 9)(x - 4)

Multiple Choice

• (x + 6)(x - 5)

• (x - 6)(x - 5)

• (x + 6)(x + 5)

• (x - 6)(x + 5)

Multiple Choice

Factor

a² - a - 12

• (a - 4)(a + 3)

• (a + 6)(a - 4)

• (a - 6)(a + 4)

• (a + 4)(a - 3)

Multiple Choice

• (x - 6)(x - 3)

• (x + 6)(x + 3)

• (x - 6)(x + 3)

• (x - 3)(x + 6)

Multiple Choice

• (x - 3)(x + 4)

• (x - 2)(x + 6)

• (x +3)(x - 4)

• (x - 6 )(x + 2)

Multiple Choice

• (x - 3)(x + 1)

• (x + 3)(x + 1)

• (x + 3)(x - 1)

• (x - 3)(x - 1)

Multiple Choice

Factor:

n² − 13n + 40

• (n − 5)(n − 8)

• (n + 5)(n − 8)

• (n − 5)(n + 8)

• (n + 6)(n + 1)

Multiple Choice

Factor:

x² – 5x – 24

• (x − 5)(x + 19)

• (x − 8)(x + 3)

• (x − 3)(x + 8)

• (x − 19)(x + 5)

Multiple Choice

Factor:

x² − 8x + 15

• (x + 5) (x + 3)

• (x − 5) (x − 3)

• (x + 15) (x − 1)

• (x − 7) (x − 8)

Multiple Choice

Factor:

x² − 15x + 50

• (x − 10)(x − 15)

• (x − 10)(x − 5)

• (x − 25)²

• (x − 5)(x − 5)

✅ Factoring Trinomials when a>1

Quick Review

Remember To first see if you have a GCF

Example

Multiple Choice

Does

$$3x^2-11x+10$$  have a GCF

• Yes

• No

No It Doesn't

So what do we do?

Slip

What two numbers multipled will give me postive 30 and sum give me -11?

Multiple Choice

What two numbers multiplied will give me positive 30 and sum give me -11?

• -1 and -30

• 5 and 6

• -5 and -6

• -2 and -15

-5 and -6

Now we are Done

Multiple Choice

Factor Completely:  3n² - 15n + 18

• (n - 2)(n - 3)
• 3(n + 2)(n + 3)
• (3n - 9)(n - 2)
• 3(n - 3)(n - 2)

Multiple Choice

Factor Completely:  6x² + 5x - 6

• 6(x + 1)(x - 6)
• (6x + 6)(x - 1)
• (2x - 3)(3x + 2)
• (3x - 2)(2x + 3)

Multiple Choice

Factor:
 4h² - 17h + 4

• (2h - 2)²
• 4(h + 4)(h + 1)
• (2h - 2)(2h + 2)
• (h - 4)(4h - 1)

Multiple Choice

Factor:
x² + 4xy + 4y²

• (x + y)(4x + 4y)
• (x + 2y)(x + 2y)
• (2x + y)(2x + y)
• (x + 2)(x + 2)

Multiple Choice

Factor
5x²-28x+32

• (3x-10)(x+6)
• (x-8)(5x-4)
• (5x-8)(x-4)
• (5x-8)(x+7)

Multiple Choice

Factor Completely:  16b² + 60b - 100

• (4b + 20)(4b - 5)
• (16b - 20)(b + 5)
• (4b + 10)(4b - 10)
• 4(b + 5)(4b - 5)

Multiple Choice

What is the GCF?

16x⁵ + 12x⁴ - x³

• x⁵

• 12x

• 6x³

• x³

Multiple Choice

Factoring reverses the process of what?

• Division
• Multiplication
• Addition
• Subtraction 

Multiple Choice

What is the GCF of the trinomial?
3x² - 9x -120

• 3
• 2
• 6
• 9

Multiple Choice

Do GCF first then factor the polynomial:  $$25h^2+125h+100$$  

• $$25\left(h+4\right)\left(h+1\right)$$  

• $$25\left(h+2\right)\left(h+2\right)$$  

• $$25\left(h+20\right)\left(h+5\right)$$  

• $$25\left(h+10\right)\left(h+10\right)$$  

Multiple Choice

What is a method of checking your work when factoring trinomials?

• FOIL
• Asking the teacher every time

• Assume you're correct

• Distributive property

Multiple Choice

Factor:
 x² - 4x + 24

• prime
• (x + 6)(x - 4)
• (x - 8)(x - 3)
• (x - 12)(x - 2)

​Factoring Trinomials + GCF

​If you can remove a Greatest Common Factor, do that before factoring a trinomial into it's binomial form

Multiple Choice

Factor completely.
3x² - 9x -120

• 3(x - 8)(x + 5)
• 3(x + 8)(x - 5)
• (3x + 8)(x - 5)
• (3x - 8)(x + 5)

Multiple Choice

Factor

3v² - 4v - 7

• (3v-7)(v+1)

• 3(v-7)(v-1)

• (3v+1)(v-9)

• (3v+1)(v-10)

Multiple Choice

Factor
9x²-6x-8

• (3x+2)(3x-4)
• (3x+2)(3x+4)
• (3x-2)(3x-4)
• (x-1)(9x+8)

Multiple Choice

What do you call a polynomial that cannot be factored?

• FOIL

• Simplified

• Prime

• Proper

Multiple Choice

Factor: $$24\ x^{2\ }-100xy+96y^{2\ }$$

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

• $$4\left(2x-3y\right)\left(3x-8y\right)$$

• $$2\left(4x-6y\right)\left(3x+8y\right)$$

• $$\left(4x-4y\right)\left(6x-24y\right)$$

Multiple Choice

Factor completely: $$-x^4y^4+8x^2y^3-7y^2$$

• $$-y^2\left(x^2y-1\right)\left(x^2y-7\right)$$

• $$y^2\left(-x^2y-1\right)\left(x^2y+7\right)$$

• $$-y^2\left(x^4y^2-8x^2y+7\right)$$

• $$y^2\left(-x^4y^2+8x^2y-7\right)$$

Multiple Choice

Factor completely: $$8b^4-20ab^3+8a^2b^2$$

• $$4b^2\left(2b^2-5ab+2a^2\right)$$

• $$b^2\left(4b-2a\right)\left(2b-4a\right)$$

• $$4b^2\left(2b-2a\right)\left(b-a\right)$$

• $$4b^2\left(2b-a\right)\left(b-2a\right)$$