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Topic 6.3.1

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.

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Topic 6.3.1

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  1. Division by Monomials Topic 6.3.1

  2. Lesson 1.1.1 Topic 6.3.1 Division by Monomials California Standard: 10.0 Studentsadd, subtract,multiply, and dividemonomials 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. • Key words: • polynomial • monomial • exponent • distributive property

  3. Rules of Exponents 1) xa·xb = xa+b 2) xa÷ xb= xa–b (if x¹ 0) 3) (xa)b = xab 4) (cx)b = cbxb 5) x0 = 1 6) x–a = (if x¹ 0) 7) 1 xa Lesson 1.1.1 Topic 6.3.1 Division by Monomials The rules of exponents that you saw in Topic 6.2.1 really are useful. In this Topic you’ll use them to divide polynomials by monomials.

  4. Lesson 1.1.1 Topic 6.3.1 Division by Monomials Dividing a Polynomial by a Monomial To dividea polynomial by a monomial, you need to use the rules of exponents. The particular rule that’s useful here is: = xa–b provided x¹ 0

  5. 2x2 2x2 ÷ x = x = xa–b provided x¹ 0 Topic 6.3.1 Division by Monomials Example 1 Divide 2x2 by x. Solution = 2x2–1 Use the rule to simplify the expression = 2x1 = 2x Solution follows…

  6. = xa–b provided x¹ 0 Topic 6.3.1 Division by Monomials Example 2 Divide 2x3y+xy2 by xy. Solution Divide each term in the expression by xy, using the distributive property = (2x3–1×y1–1) + (x1–1×y2–1) Simplify using the rule =(2x2× 1) + (1 ×y1) =2x2 +y Solution follows…

  7. Simplify . Topic 6.3.1 Division by Monomials Example 3 Solution = (–1×m3–1) – (–2×m2–1×c3–2) + (–5×c4–2×v3–1) = –m2 + 2mc – 5c2v2 Solution follows…

  8. Lesson 1.1.1 Topic 6.3.1 Division by Monomials Guided Practice Simplify each of these quotients. 1. 9m3c2v4 ÷ (–3m2cv3) 2. 3. –3m3 – 2c2 – 1v4 – 3 = –3mcv 3x5 – 3y6 – 5z4 – 2 = 3x2yz2 2m3 – 3x2 – 2 – 3m4 – 3x3 – 2 = 2 – 3mx Solution follows…

  9. Lesson 1.1.1 Topic 6.3.1 Division by Monomials Guided Practice Simplify each of these quotients. 4. 5. 6. –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 Solution follows…

  10. Topic 6.3.1 Division by Monomials Independent Practice Simplify each of these quotients. 1. 2. 3. 4. –2x2 + x – 3 2x3 – x2 + 3x – 5 3mv2 – cv + 4 4yz + 8xy2z2 Solution follows…

  11. Topic 6.3.1 Division by Monomials Independent Practice 5. Divide 15x5 – 10x3 + 25x2 by –5x2. –3x3 + 2x – 5 6. Divide 20a6b4 – 14a7b5 + 10a3b7 by 2a3b4. 10a3 – 7a4b + 5b3 7. Divide 4m5x7v6 – 12m4c2x8v4 + 16a3m6c2x9v7 by –4m4x7v4. –mv2 + 3c2x – 4a3m2c2x2v3 Solution follows…

  12. Topic 6.3.1 Division by Monomials Independent Practice Find the missing exponent in the quotients. 8. 9. ? = 3 ? = 4 Solution follows…

  13. Topic 6.3.1 Division by Monomials Round Up 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.

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