Factoring L2.4

Presentation

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Mathematics

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10th - 12th Grade

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Easy

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CCSS

HSA.SSE.A.2, HSA.APR.C.4, HSA.APR.A.1

Standards-aligned

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17 Slides • 25 Questions

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)

Factoring

Lesson 2.4

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