1

Math 50

3.6 – Introduction to Factoring

2

Since , we know that .

In general, ________________ the exponents when dividing exponential factors with same base.

So, for ,

Dividing Monomials

3

Since , we know that .

In general, ________________ the exponents when dividing exponential factors with same base.

So, for ,

Dividing Monomials

4

Since , we know that .

In general, ________________ the exponents when dividing exponential factors with same base.

So, for ,

Dividing Monomials

subtract

5

Since , we know that .

In general, ________________ the exponents when dividing exponential factors with same base.

So, for ,

Dividing Monomials

subtract

6

Since , we know that .

In general, ________________ the exponents when dividing exponential factors with same base.

So, for ,

Dividing Monomials

subtract

Ex 1.Divide:

7

Since , we know that .

In general, ________________ the exponents when dividing exponential factors with same base.

So, for ,

Dividing Monomials

subtract

Ex 1.Divide:

8

Notice that but also

In general, for , (Note: is _____________________)

9

Notice that but also

In general, for , (Note: is _____________________)

10

Notice that but also

In general, for , (Note: is _____________________)

11

Notice that but also

In general, for , (Note: is _____________________)

12

Notice that but also

In general, for , (Note: is _____________________)

13

Notice that but also

In general, for , (Note: is _____________________)

So,

14

Notice that but also

In general, for , (Note: is _____________________)

So,

15

Notice that but also

In general, for , (Note: is _____________________)

So,

indeterminate

16

Ex 2.Simplify (assume ): Ex 3.Simplify:

17

Ex 2.Simplify (assume ): Ex 3.Simplify:

18

Ex 2.Simplify (assume ): Ex 3.Simplify:

19

Ex 2.Simplify (assume ): Ex 3.Simplify:

20

Ex 2.Simplify (assume ): Ex 3.Simplify:

21

Ex 2.Simplify (assume ): Ex 3.Simplify:

22

To divide monomials with same variable:1. ___________ coefficients.2. _____________ exponents of variables (top exponent minus bottom exponent). Ex 4.Divide: Ex 5.Divide:

Dividing Monomials

23

To divide monomials with same variable:1. ___________ coefficients.2. _____________ exponents of variables (top exponent minus bottom exponent). Ex 4.Divide: Ex 5.Divide:

Dividing Monomials

Divide

24

To divide monomials with same variable:1. ___________ coefficients.2. _____________ exponents of variables (top exponent minus bottom exponent). Ex 4.Divide: Ex 5.Divide:

Dividing Monomials

DivideSubtract

25

To divide monomials with same variable:1. ___________ coefficients.2. _____________ exponents of variables (top exponent minus bottom exponent). Ex 4.Divide: Ex 5.Divide:

Dividing Monomials

DivideSubtract

147 6−2

26

To divide monomials with same variable:1. ___________ coefficients.2. _____________ exponents of variables (top exponent minus bottom exponent). Ex 4.Divide: Ex 5.Divide:

Dividing Monomials

DivideSubtract

147 6−2

13−132−4

27

Since ,we know that .

If we wanted to divide by (without knowing the answer), we could divide each term by . It would look like this:

In general, to divide a polynomial by a monomial, divide each term by the monomial.

Divide Polynomial by Monomial

28

Since ,we know that .

If we wanted to divide by (without knowing the answer), we could divide each term by . It would look like this:

In general, to divide a polynomial by a monomial, divide each term by the monomial.

Divide Polynomial by Monomial

29

Since ,we know that .

If we wanted to divide by (without knowing the answer), we could divide each term by . It would look like this:

In general, to divide a polynomial by a monomial, divide each term by the monomial.

Divide Polynomial by Monomial

30

Since ,we know that .

If we wanted to divide by (without knowing the answer), we could divide each term by . It would look like this:

In general, to divide a polynomial by a monomial, divide each term by the monomial.

Divide Polynomial by Monomial

31

Ex 6.Divide: Ex 7.Divide:

Divide Polynomial by Monomial

32

Ex 8.Find the unknown factor: Ex 9.Find the unknown factor:

Find Unknown Factor

33

When a number or expression is written as product of factors it is in __________________.

ex: is factored form for

34

When a number or expression is written as product of factors it is in __________________.

ex: is factored form for

factored form

35

When a number or expression is written as product of factors it is in __________________.

ex: is factored form for

factored form

36

1. Find GCF of terms of polynomial.2. Rewrite polynomial like this:

3. Divide inside the parentheses.

How to factor monomial GCF out of a polynomial

37

Ex 10.Factor:

Ex 11.Factor:

38

Summary: (ex: )

(ex: )

Divide monomials:1. Divide coefficients, 2. Subtract exponents. (ex: )

Factor out GCF:1. Find GCF, 2. , 3. Divide.