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Division by Monomials. Topic 6.3.1. Lesson 1.1.1. Topic 6.3.1. Division by Monomials. California Standard: 10.0 Students add, subtract, multiply, and divide monomials and polynomials . Students solve multistep problems, including word problems, by using these techniques. - PowerPoint PPT Presentation
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Topic 6.3.1Topic 6.3.1
Division by MonomialsDivision by Monomials
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Lesson
1.1.1
California Standard:10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.
What it means for you:You’ll learn how to use the rules of exponents to divide a polynomial by a monomial.
Division by MonomialsDivision by MonomialsTopic
6.3.1
Key words:• polynomial• monomial• exponent• distributive property
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Lesson
1.1.1
The rules of exponents that you saw in Topic 6.2.1 really are useful.
Division by MonomialsDivision by MonomialsTopic
6.3.1
In this Topic you’ll use them to divide polynomials by monomials.
1) xa·xb = xa+b 2) xa ÷ xb = xa–b (if x 0)
3) (xa)b = xab 4) (cx)b = cbxb
5) x0 = 1 6) x–a = (if x 0)
7)
xa1
Rules of Exponents
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Lesson
1.1.1
Dividing a Polynomial by a Monomial
Division by MonomialsDivision by MonomialsTopic
6.3.1
To divide a polynomial by a monomial, you need to use the rules of exponents.
The particular rule that’s useful here is:
= xa–b provided x 0
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Division by MonomialsDivision by Monomials
Example 1
Topic
6.3.1
Divide 2x2 by x.
Solution
Solution follows…
2x2
x2x2 ÷ x =
= xa–b provided x 0
Use the rule to simplify the expression
= 2x
= 2x1
= 2x2–1
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= (2x3–1 y1–1) + (x1–1 y2–1)
Division by MonomialsDivision by Monomials
Example 2
Topic
6.3.1
Divide 2x3y + xy2 by xy.
Solution
Solution follows…
Divide each term in the expression by xy, using the distributive property
= 2x2 + y
= (2x2 1) + (1 y1)
Simplify using the rule
= xa–b provided x 0
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Division by MonomialsDivision by Monomials
Example 3
Topic
6.3.1
Solution
= (–1m3–1) – (–2m2–1c3–2) + (–5c4–2v3–1)
Solution follows…
Simplify .
= –m2 + 2mc – 5c2v2
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Lesson
1.1.1
Guided Practice
Division by MonomialsDivision by MonomialsTopic
6.3.1
Solution follows…
Simplify each of these quotients.
1. 9m3c2v4 ÷ (–3m2cv3)
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3.
–3m3 – 2c2 – 1v4 – 3 = –3mcv
3x5 – 3y6 – 5z4 – 2 = 3x2yz2
2m3 – 3x2 – 2 – 3m4 – 3x3 – 2 = 2 – 3mx
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Lesson
1.1.1
Guided Practice
Division by MonomialsDivision by MonomialsTopic
6.3.1
Solution follows…
Simplify each of these quotients.
4.
5.
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–2x4 – 3y5 – 3t3 – 2 + 4x3 – 3y4 – 3t2 – 2 + x5 – 3y3 – 3t3 – 2
= –2xy2t + 4y + x2t
–2x5 – 4y8 – 3a4 – 0z12 – 9
= –2xy5a4z3
–2a9 – 5d1 – 1f 9 – 0k3 – 2 + 3a8 – 5d6 – 1f 5 – 0k3 – 2 – 7c1 – 0a8 – 5d8 – 1k4 – 2
= –2a4f 9k + 3a3d5f 5k – 7ca3d7k2
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Division by MonomialsDivision by Monomials
Independent Practice
Solution follows…
Topic
6.3.1
Simplify each of these quotients.
1.
2.
3.
4.
–2x2 + x – 3
2x3 – x2 + 3x – 5
3mv2 – cv + 4
4yz + 8xy2z2
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Division by MonomialsDivision by Monomials
Independent Practice
Solution follows…
Topic
6.3.1
5. Divide 15x5 – 10x3 + 25x2 by –5x2.–3x3 + 2x – 5
6. Divide 20a6b4 – 14a7b5 + 10a3b7 by 2a3b4.
7. Divide 4m5x7v6 – 12m4c2x8v4 + 16a3m6c2x9v7 by –4m4x7v4.
10a3 – 7a4b + 5b3
–mv2 + 3c2x – 4a3m2c2x2v3
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Division by MonomialsDivision by Monomials
Independent Practice
Solution follows…
Topic
6.3.1
Find the missing exponent in the quotients.
8.
9.
? = 3
? = 4
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Topic
6.3.1
Round UpRound Up
Division by MonomialsDivision by Monomials
This leads on to the next few Topics, where you’ll divide one polynomial by another polynomial.
First, you’ll learn how to find the multiplicative inverse of a polynomial in Topic 6.3.2.
