357: Choose a Factoring Method Lesson

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 + 35a⁴b² is:

• 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