Factoring using Distributive Property

3/10/10

Factoring Using Distributive Property

Steps: Ex1) 5x +10• Step 1: Examine ? Common

NumberNotice 5 is

a multiple of both

• Step 2: Remove 5(x + 2)

Factoring Using Distributive Property

• Practice: Yes or No – There is a common multiple that can be

removed?

1. 4x – 10

2. 3x – 7

3. x2 + 2x

4. x2 + 4

Yes 2, 2(x - 5)

No, 3x - 7

Yes x, x(x + 2)

No, (x2 + 4)

Factoring Using Distributive Property

So far we’ve used distributive property for simple binomials, but you can alsouse it for polynomials.

Example 2) 4ab + 8b + 3a + 6

First group the monomialsto make groups with commonmultiples:

(4ab + 8b) + (3a + 6)

Remove the common monomial: 4b(a + 2) + 3(a + 2)

Associate Property(4b + 3)(a + 2)

4b(a + 2) + 3(a + 2)

Factoring Using Distributive Property

So far we’ve used distributive property for simple binomials, but you can alsouse it for polynomials.

Example 3) c – 2cd + 8d - 4

First group the monomialsto make groups with commonmultiples:

(c – 2cd) + (8d - 4)

Remove the common monomial: c(1 - 2d) - 4(-2d + 1)

Associate Property(c – 4)(1 – 2d)

c(1 – 2d) - 4(-2x + 1)

Factoring Using Distributive Property

• Practice: Factor the following:

1. 3p – 2p2 – 18p + 27

2. 3p2q – 9pq2 + 36pq

(p + 9)(-2p + 3)

3pg(p – 3q + 12)

Now that we know: c – 2cd + 8d - 4 factors to (c – 4)(1 – 2d) we can

solve.

c – 2cd + 8d – 4 = 0 or(c – 4)(1 – 2d) = 0

(c – 4) = 0 and (1-2d) = 0 c = 4 -2d = -1 d = 1/2

Factoring Using Distributive Property

If we wanted to check our answer you can sub c=4 and d=1/2 back into the problem

Lets put it all togetherx2 – 24x = 0x(x – 24) = 0x = 0 and x-24 = 0 x = 24

So x = 0,24

Factoring Using Distributive Property

If we wanted to check our answer you can sub c=4 and d=1/2 back into the problem

Lets put it all together 2 5y2 – 15y +4y = 125y2 – 15y + 4y -12 = 0 Make it equal to 0

(5y2 – 15y) + (4y-12) = 05y(y – 3) + 4(y – 3) = 0(5y + 4)(y – 3) = 0

5y + 4 = 0 y – 3 = 05y = -4 y = 3y = -4/5

y = -4/5, 3

Factoring Using Distributive Property

Reminder: To check your workyou can always input your answerback into the original problem.

Homework

Factoring Using Distributive Property