Factoring Complex Trinomials (2021)

Factoring Complex Trinomials (2021)

by Mr. Ternet

​Steps for Factoring Complex Trinomials

​1. Multiply the 1^st and last numbers

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​2. Create a simple trinomial

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3. Factor this trinomial into 2 sets of ( )

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4. Insert the 1^st coefficient into each set of ( )

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​5. Reduce/Simplify each ( ) if necessary

STEP 1: Multiply the 1^st and last numbers​

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Multiple Choice

If you were asked to factor $$3x^2-2x-5$$  

What would you do first?

• Multiply 3 and -2

• Multiply 3 and -5

• Multiply -2 and -5

• Multiply 3, -2 and -5

STEP 2: Create a simple trinomial​

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Multiple Choice

If you were asked to factor $$3x^2-2x-5$$  

After multiplying, the product is -15, what is the new simple trinomial?

• $$x^2-2x-15$$  

• $$x^2-2x+15$$  

• $$x^2-15$$  

• $$x^2+15$$  

STEP 3: Factor the simple trinomial​

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Multiple Select

What are the two sets of ( ) when factoring $$x^2-2x-15$$  ?

(select 2)

• $$\left(x+5\right)$$  

• $$\left(x-5\right)$$  

• $$\left(x+3\right)$$  

• $$\left(x-3\right)$$  

STEP 4: Insert the 1st coefficient into both sets of ( )​

Multiple Choice

If the original trinomial was $$3x^2-2x-5$$  , what number would you add to each set of ( )?

• 3

• -2

• -5

STEP 5: Simplify/Reduce each set of ( )​

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Multiple Choice

If you have $$\left(3x+5\right)$$   as one of your ( ), can it reduce?

• YES

• NO

Multiple Choice

If you have $$\left(3x+3\right)$$  as one of your ( ), can it be reduced?

• YES

• NO

Multiple Choice

What does $$\left(3x+3\right)$$   reduce to?

• $$\left(x+1\right)$$  

• $$\left(3x+1\right)$$  

• $$\left(x+3\right)$$  

​Steps for Factoring Complex Trinomials

​1. Multiply the 1^st and last numbers

​

​2. Create a simple trinomial

​

3. Factor this trinomial into 2 sets of ( )

​

4. Insert the 1^st coefficient into each set of ( )

​

​5. Reduce/Simplify each ( ) if necessary

Multiple Choice

Now, try to factor this trinomial on your own.

$$3x^2-8x+4$$  

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

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

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

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