1. 9-2 Multiplying and Factoring Monomials

2. Multiplying by a Monomial
We have already multiplied a number by a polynomial.
5(3x2 + 6x – 7)
Distribute!
15x2

3. Multiplying by a Monomial
We have already multiplied a number by a polynomial.
5(3x2 + 6x – 7)
Distribute!
15x2 + 30x

4. Multiplying by a Monomial
We have already multiplied a number by a polynomial.
5(3x2 + 6x – 7)
Distribute!
15x2 + 30x – 35
Nothing changes just because we added variables.

5. Multiplying by a Monomial
We have already multiplied a number by a polynomial.
5(3x2 + 6x – 7)
Distribute!
15x2 + 30x – 35
Nothing changes just because we added variables.
3x2(2x2 – 5x + 1)

6. Multiplying by a Monomial
We have already multiplied a number by a polynomial.
5(3x2 + 6x – 7)
Distribute!
15x2 + 30x – 35
Nothing changes just because we added variables.
3x2(2x2 – 5x + 1)
6x4

7. Multiplying by a Monomial
We have already multiplied a number by a polynomial.
5(3x2 + 6x – 7)
Distribute!
15x2 + 30x – 35
Nothing changes just because we added variables.
3x2(2x2 – 5x + 1)
6x4 – 15x3

8. Multiplying by a Monomial
We have already multiplied a number by a polynomial.
5(3x2 + 6x – 7)
Distribute!
15x2 + 30x – 35
Nothing changes just because we added variables.
3x2(2x2 – 5x + 1)
6x4 – 15x3 + 3x2

9. Finding Your “Good Close Friend”
When trying to simplify a polynomial, finding your GCF (greatest common factor) is your first line of defense.
10x4 – 5x2 +15
What is “common” to all 3 terms? 5
So, we take out the common thing. 5(

10. Finding Your “Good Close Friend”
When trying to simplify a polynomial, finding your GCF (greatest common factor) is your first line of defense.
10x4 – 5x2 +15
What is “common” to all 3 terms? 5
So, we take out the common thing.
5(2x4

11. Finding Your “Good Close Friend”
When trying to simplify a polynomial, finding your GCF (greatest common factor) is your first line of defense.
10x4 – 5x2 +15
What is “common” to all 3 terms? 5
So, we take out the common thing.
5(2x4 – x2

12. Finding Your “Good Close Friend”
When trying to simplify a polynomial, finding your GCF (greatest common factor) is your first line of defense.
10x4 – 5x2 +15
What is “common” to all 3 terms? 5
So, we take out the common thing.
5(2x4 – x2 + 3)
This is called the “factored form”

13. Finding Your “Good Close Friend”
3x4 + 9x2 +12x
What is “common” to all 3 terms? 3x
So, we take out the common thing.
3x(

14. Finding Your “Good Close Friend”
3x4 + 9x2 +12x
What is “common” to all 3 terms? 3x
So, we take out the common thing.
3x(x3

15. Finding Your “Good Close Friend”
3x4 + 9x2 +12x
What is “common” to all 3 terms? 3x
So, we take out the common thing.
3x(x3 + 3x

16. Finding Your “Good Close Friend”
3x4 + 9x2 +12x
What is “common” to all 3 terms? 3x
So, we take out the common thing.
3x(x3 + 3x +4)

17. Example #1
Multiply:
3x2(-8x + 2)

18. Example #1
Multiply:
3x2(-8x + 2) = -24x3

19. Example #1
Multiply:
3x2(-8x + 2) = -24x3 + 6x2

20. Example #2
Factor: 4x3 – 2x2

21. Example #2
Factor: 4x3 – 2x2 = 2x2(

22. Example #2
Factor: 4x3 – 2x2 = 2x2(2x

23. Example #2
Factor: 4x3 – 2x2 = 2x2(2x – 1)

24. Today’s Assignment
P. 501 #1-31 odds