Factoring L2.4

Factoring

Lesson 2.4

Always look for a GCF first

notice what is in parenthesis has nothing in common

Another example:

 $4x^2y-10xy^2+2xy$  
 $=2xy\left(2x-5y+1\right)$  

Multiple Choice

Factor by GCF:

18a²-15a

• 15a(3a-1)

• 3a(6a-1)

• 3(6a-5)

• 3a(6a-5)

Multiple Choice

Factor:
2n³+16n+12

• 2n(n³+24n+6)
• 2(n³+8n+6)
• 2n(n³+8n+6)
• 3(n³+8n+6)

DOTS

Difference of 2 Squares

The factors will always be

a CONJUGATE PAIR

Multiple Choice

16n² - 25

• (16n - 25)(16n + 25)
• (8n - 5)(8n + 5)
• (4n + 5)(4n - 5)
• Not Factorable

Multiple Choice

x² + 81

• not factorable

• ( x - 9 ) ( x + 9 )

• ( x + 9 ) ( x + 9 )

• ( x - 9 ) ( x - 9 )

The SUM of Squares is NOT factorable. Signs must be opposite, so the middle terms will cancel.

Multiple Choice

Factor:
x² - 9

• ( x -9) (x - 9)
• (x + 3) (x + 3)
• (x + 3) (x - 3)
• ( x + 9) (x-9)

Let's combine GCF and DOTS!

Study the example--->

Take the GCF out First

Multiple Choice

Factor completely:  $50x^3-18x^{ }$  

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

•  $x\left(50x^2-18\right)$  

•  $900x^4$  

•  $2\left(25x^3-9x\right)$  

Multiple Choice

Factor the Following completely

4x²-16

• (2x-4)(2x+4)

• (4x-4)(4x+4)

• 4(x-2)²

• 4(x-2)(x+2)

DOC and SOC

The patterns are the same except for the signs!

Multiple Choice

Factor:   x³ + 1

• (x + 1)³
• (x+1)(x² - x + 1)
• (x - 1) (x² + x - 1)
• (x + 1)(x² - 2x + 1)

Multiple Choice

Factor
27x³-64

• (3x-4)(9x²+12x+16)
• (3x-4)(9x²-12x+16)
• (3x+4)(9x²-12x+16)
• (3x+4)(9x²+12x+16)

Multiple Choice

Factor:  27x³ + 8

• (3x + 2)(9x² - 6x + 4)
• (9x + 2)(3x² + 18x + 4)
• (3x²+4)(9x + 2)
• (27x + 8)(x² - 216x + 64)

Multiple Choice

Factor: 8x³ - 1

• (2x - 1)(4x² + 2x + 1)
• (2x + 1)(4x² - 2x + 1)
• (2x - 1)(4x² - 2x - 1)
• (2x + 1)(4x² +2x + 1)

Hey you...Pay attention to the next slide.

Perfect Square Trinomials

The first and last terms will be perfect squares. The middle will be 2ab.

Example:

Notice the middle term comes from 2ab:

2(2x)(5) = 20x

Multiple Choice

FACTOR:  $16x^2-40xy+25y^2$  

•  $\left(5x-4y\right)^2$  

•  $\left(8x+5y\right)^2$  

•  $\left(4x-5y\right)^2$  

• NOT FACTORABLE

Multiple Choice

FACTOR:  $x^2-9x+9$  

•  $\left(x-9\right)^2$  

•  $\left(x-3\right)^2$  

•  $\left(x+3\right)^2$  

• NOT FACTORABLE

Multiple Choice

Fill in the blank to make

 $b^2-\left(?\right)+36$  a Perfect Square Trinomial (PST)

•  $2b$  

•  $6b$  

•  $12b$  

•  $-b$  

Multiple Choice

Factor:

16b² + 24b + 9

• (8b + 3)²

• (3b + 4)²

• (4b + 3)²

a = 1

easy peasy!

What multiplies to = c

and adds to = b ???

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
k² -2k - 24

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

Multiple Choice

Find the expression equivalent
to (x-1)(x-9)

• x²+9
• x²-10x+9
• x²-10x-9
• x²+10x+9

On the next problem, look for a GCF first. Then, factor the a = 1 expression

Multiple Choice

Factor Completely: 2k²-14k-60

• 2(k-10)(k-3)
• Not Factorable
• (k-5)(k+9)
• 2(k-10)(k+3)

 $When\ a\ \ne1$  

1. Multiply ac
2. Factors of ac that add to 'b'
3. Split middle term to make 4
4. Group and take out GCFs
(Parentheses much match!)
Answer: (3x-2)(2x+5)

Here's another method:

Slide, Divide, Bottoms Up!

One More Method:

when you have multiple choice, it might be easier to just pick out the right answer!

Multiple Choice

Factor
4n²-17n-15

• (n-10)(6n+1)
• (4n-5)(n-3)
• (n-5)(4n-3)
• (n-5)(4n+3)

Multiple Choice

Factor:
 2m² + 3m - 9

• 2(m + 3)(m - 3)
• (2m - 3)²
• (m + 3)(2m - 3)
• (2m + 3)(m - 3)

Multiple Choice

Factor completely: 2x² - 3x - 2

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

Multiple Choice

Factor Completely: 6x² + 7x - 3

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

Grouping

when you have 4 terms

Careful with the signs

when there seems to be no GCF,

use a 1

Multiple Choice

What is the factored form of x³+7x²-2x-14

• (x²-2)(x-7)

• (x²+2)(x-7)

• (x²+2)(x+7)

• (x²-2)(x+7)

Multiple Choice

What is the factored form of 5n³-10n²+3n-6

• (5n²+3)(n-2)
• (5n²-3)(n-2)
• (5n³+3)(n-2)
• 10n(n²-6)