Factoring Methods

Presentation

•

Mathematics

•

9th Grade

•

Hard

Joseph Anderson

FREE Resource

7 Slides • 12 Questions

Choose a Factoring Method

I can identify the appropriate factoring method given a polynomial.

Multiple Choice

First step of Factoring is

Finding the GCF

Divide by the GCF

Multiply by the GCF

Subtract by the GCF

Multiple Choice

Factor (GCF):
12x + 9

3 (4x + 3)

x (12+9)

3 (4x - 3)

Prime

Multiple Choice

The G.C.F of the expression 30a³b² + 20a²b + 35a⁴b²is:

30a⁴b²

20a⁴b²

5a²b

5a⁴b²

Difference of Squares

Are there two terms (binomial)?

Does it have degree = 2?

Is it a difference?

Are both terms Perfect Squares?

Multiple Choice

x²- 25

( x + 5 ) ( x - 5 )

( x - 5 ) ( x - 5 )

( x + 5 ) ( x + 5 )

Unfactorable

Multiple Choice

x²- 225

( x + 15) ( x + 15)

Unfactorable

( x - 15) ( x + 15)

( x - 15) ( x - 15)

Multiple Choice

4x²- 64y²

Unfactorable

( 2x - 32y) (2 x + 32y)

( 2x - 8y) (2 x - 8y)

( 2x - 8y) (2 x + 8y)

Trinomials (a=1 & a>1)

Identify a, b, and c

Multiply a and c

Find the factors of ac that sum to b

(use the X strategy for organizing)

Now you have 4 terms and you can factor by grouping using the box method.

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
x² + 4x + 3

(x - 1)(x - 3)

(x + 1)(x + 3)

(x - 1)(x + 3)

(x + 1)(x - 3)

Multiple Choice

Factor

4x²-25x+25

4(x-5)(x+5)

(x+5)(4x+5)

(x-5)(4x-5)

(x+2)(9x+1)

Multiple Choice

Factor
3a² + 4a + 1

(7a-10)(a-8)

Not factorable

(3a+1)(a+1)

(3a-1)(a-1)

Factor by Grouping (Box Method)

Draw a box

Put each term in a box in order

Find the GCF of each column and each row

If there is no GCF, then write 1

If there is a negative in the first box, then the GCF should be negative

Multiple Choice

Factor by grouping:
5n³-10n²+3n-6

(5n²+3)(n-2)

(5n²-3)(n-2)

(5n³+3)(n-2)

10n(n²-6)

Multiple Choice

Factor by grouping:

4p³+8p²+3p+6

(2p²+3)(p+2)

(2p²+6)(p+4)

(4p²+3)(p+2)

(4p²+8p)(3p+6)

Summary

Factor out GCF (if needed)
Decide which method by the number of terms
2 terms - Check for DIFFERENCE OF SQUARES
3 terms - Use the ac method for finding factors, then the box method
4 terms - Use the box method
Write your answer as a series of binomial products
Put the GCF from Step 1 (if you had one) out front

Choose a Factoring Method

I can identify the appropriate factoring method given a polynomial.

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