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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