8­5 Using the Distributive Property.notebook
8­5 Using the Distributive Property
Goals:
1. Use the Distributive Property to factor polynomials.
February 08, 2014
Factoring ­ to express a polynomial as the product of monomials and polynomials.
Factoring breaks up a polynomial equations into parts that multiply together to make the whole.
2. Solve equations of the form of ax2+bx=0
In these problems, we are going to use the "reverse" distributive property by taking OUT what is in common in all of the terms.
OUT
27y2+18y
9
y
Use the Distributive Property to factor the polynomial.
15w ­ 3v
What number is common to 27 and 18? (GCF) What variable is common to y2 and y?
3(5w­v)
Answer: 9y
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8­5 Using the Distributive Property.notebook
Use the Distributive Property to factor the polynomial.
February 08, 2014
Factoring by Grouping ­
when you have 4 terms
Put the terms into groups, then factor.
7u2t2+21ut2­ut
ut(7ut+21t­1)
Factor (by grouping)
4qr +8r +3q +6
Factor the polynomial: c ­2cd+8d ­4
1. Group the first two terms and the last two terms
(4qr +8r) +(3q +6)
2. Take out what is in common in the 1st group
4r(q +2)
3. Take out what is in common in the 2nd group
+3(q +2)
4. Put the common ( ) together and put what is left together.
(c ­4)(1­ 2d)
(q +2) (4r +3)
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8­5 Using the Distributive Property.notebook
Factor the polynomial: 3p ­2p2 ­18p +27
February 08, 2014
Solve equations by factoring using the Zero Product Property.
(p +9)(3­2p)
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8­5 Using the Distributive Property.notebook
February 08, 2014
Solve the equation. Check your solutions.
Solve the equation. Check your solutions.
3n(n +2)=0
8b2 ­40b =0
0, ­2
0, 5
Solve the equation. Check your solutions.
x2 = ­10x
0, ­10
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8­5 Using the Distributive Property.notebook
February 08, 2014
8­5 Assignment
Page: 498: 15 ­42 every 3rd problem, 46, 48
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