Factoring Lesson

Factoring Lesson

​Make sure you're ready with paper and pencil to take notes on the following problems!

​Reviewing The Basics

We know (and recently reviewed for dividing polynomials) that when you multiply the two outside factors, you find the area inside a box.

​We're going to be given the area inside and will find the factors that multiply to make it!

​The difference from division is that when factoring, it always works!!

Multiple Choice

Factor:  x² - 2x - 24

• (x + 6)(x - 4)
• (x + 4)(x - 6)
• (x - 4)(x - 6)

• (x - 3)(x + 8)

​Remember:

​ALWAYS look for a GCF first!

​

GCF: Greatest Common Factor

​

​If you can divide a common factor out, it makes the rest of the problem much easier to do!

Multiple Choice

What is the GCF of 18 and 45?

• 3

• 12

• 9

• 6

Multiple Choice

What is the GCF of the trinomial? 3x³ - 9x -120x²

• 3x

• 27

• 3

• none

Multiple Choice

Factor out the GCF of 10x + 50

• 10(10x+50)
• 10(x+50)
• 10(x+5)
• Cannot be factored

​Once you've found the GCF...

Factor it out! Then what's left goes in our area model box!

​

​Let's do this one together!

​What is the GCF?

​

​(Don't forget to write this one down)

Now let's keep going!​

​Now that we've factored out the 3:

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​Let's use the area model for the quadratic in the parentheses!

​

​

​Final Way to write it!

​Remember to add that 3 back in front!

​

​It doesn't matter the order of the factors, just be careful with your signs staying with the right numbers!

Multiple Choice

Factor:
 2n²-8n³

• 2n²(n-4n²)
• 2n²(1-4n)

• 2n³(10-8n²)
• 3n(1-4n)

Multiple Choice

Factor completely: 
3x² + 18x +15
Hint: Factor GCF first.

• 3(x² + 6x + 5)
• (x + 5)(x + 1)
• 3(x + 5)(x + 1)
• Prime

Multiple Choice

Factor the trinomial 2x²+10x+12

• 2(x+3)(x+2)

• (x+3)(x+2)

• 2(x+6)(x+1)

• 2(x+5)(x+1)

​Let's Review the ENTIRE Process

1. Always look for a GCF and factor it out if it exists

2. ​Then, put your first term in the first box and the last term in the last box (because we know with factoring we won't have remainders!!)

3. ​Find the diagonal product and list its factors

4. ​Choose the factor pair that adds to the middle term and multiplies to our DP

5. ​Find each row and column's GCF

6. ​Write the full answer out!

Do it again!!

1. Always look for a GCF and factor it out if it exists

2. ​Then, put your first term in the first box and the last term in the last box (because we know with factoring we won't have remainders!!)

3. ​Find the diagonal product and list its factors

4. ​Choose the factor pair that adds to the middle term and multiplies to our DP

5. ​Find each row and column's GCF

6. ​Write the full answer out!

YUP! AGAIN!!

1. Always look for a GCF and factor it out if it exists

2. ​Then, put your first term in the first box and the last term in the last box (because we know with factoring we won't have remainders!!)

3. ​Find the diagonal product and list its factors

4. ​Choose the factor pair that adds to the middle term and multiplies to our DP

5. ​Find each row and column's GCF

6. ​Write the full answer out!

Let's Practice!!​