Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

9.4.1

299 views

Published on

  • Be the first to comment

  • Be the first to like this

9.4.1

  1. 1. Dividing by a MonomialWrite the division as a fraction and use the quotient of powers property.When dividing polynomials, you can check your work using multiplication.
  2. 2. Example 1 Divide monomialsDivide – 8x5 by 2x2.SOLUTIONWrite the division as a fraction and use the quotientof powers property. – 8x5 – 8x5 ÷ (2x2 ) = Write as fraction. 2x2 – 8 x5 Rewrite using product rule for = • 2 fractions. 2 x –8 = • x5 – 2 Quotient of powers property 2
  3. 3. Example 1 Divide monomials = – 4x3 Simplify.
  4. 4. Example 2 Multiple Choice Practice4x3 =16x 8 1 x5 1 4x 5 4x5 12 12x54x3 4 x3 = • 8 Rewrite using product rule for16x 8 16 x fractions. 1 Quotient of powers property = • x– 5 4 1 1 Definition of negative exponents = • 5 4 x
  5. 5. Example 2 Multiple Choice Practice 1 Simplify. = 5 4xANSWER The correct answer is B.
  6. 6. Example 3 Divide a polynomial by a monomialDivide 4x3 + 8x2 + 10x by 2x.SOLUTION 4x3 + 8x2 + 10x( 4x3 + 8x2 + 10x ) ÷ 2x = Write as fraction. 2x 4x3 8x2 10x = + + Divide each term 2x 2x 2x by 2x. = 2x2 + 4x + 5 Simplify.
  7. 7. Example 3 Divide a polynomial by a monomialCHECK Check to see if the product of 2x and 2x2 + 4x + 5 is 4x3 + 8x2 + 10x. ? ( 2x2 + 4x + 5) = 4x3 + 8x2 + 10x 2x ? 2x ( 2x2 ) + 2x (4x ) + 2x (5 ) = 4x3 + 8x2 + 10x 4x3 + 8x2 + 10x = 4x3 + 8x2 + 10x
  8. 8. Division with Algebra TilesPg. 540
  9. 9. Dividing by a BinomialTo divide a polynomial by a binomial, use long division.
  10. 10. Example 4 Divide a polynomial by a binomialDivide x2 + 2x – 3 by x – 1.SOLUTIONSTEP 1 Divide the first term of x2 + 2x – 3 by the first term of x – 1. x x – 1 x2 + 2x – 3 Think: x2 ÷ x = ? x2 – x Multiply x – 1 by x. 3x Subtract x2 – x from x2 + 2x.
  11. 11. Example 4 Divide a polynomial by a binomialSTEP 2 Bring down –3. Then divide the first term of 3x – 3 by the first term of x – 1. x + 3 x – 1 x2 + 2x – 3 x2 – x 3x – 3 Think: 3x ÷ x = ? 3x – 3 Multiply x – 1 by 3. 0 Subtract 3x – 3 from 3x – 3; remainder is 0.ANSWER ( x2 + 2x – 3) ÷ (x – 1) = x + 3
  12. 12. Nonzero Remainders When you obtain a nonzero remainder, apply the following rule: Re mainder Dividend ÷ Divisor = Quotient + Divisor 2 2 5 ÷ 1+ 3 = Which is really 1 3 3 12(2 x + 11x − 9) ÷ ( 2 x − 3) = x + 7 + 2 2x − 3
  13. 13. Example 5 Divide a polynomial by a binomialDivide 2x2 + 11x – 9 by 2x – 3. x + 7 2x – 3 2x2 + 11x – 9 2x2 – 3x Multiply 2x – 3 by x. 14x – 9 Subtract 2x2 – 3x. Bring down – 9. 14x – 21 Multiply 2x – 3 by 7. 12 Subtract 14x – 21; remainder is 12. 12ANSWER (2x + 11x – 9) ÷ ( 2x – 3) = x + 7 + 2 2x – 3
  14. 14. Example 6 Rewrite polynomialsDivide 5y + y2 + 4 by 2 + y. y + 3 y + 2 y2 + 5y + 4 Rewrite polynomials. y2 + 2y Multiply y + 2 by y. 3y + 4 Subtract y2 + 2y. Bring down 4. 3y + 6 Multiply y + 2 by 3. –2 Subtract 3y + 6; remainder is – 2. –2ANSWER (5y + y + 4) ÷ ( 2 + y) = y + 3 + 2 y +2
  15. 15. Example 7 Insert missing termsDivide 13 + 4m2 by –1 + 2m. 2m + 1 Rewrite polynomials. Insert 2m – 1 4m2 + 0m + 13 missing term. 4m2 – 2m Multiply 2m – 1 by 2m. 2m + 13 Subtract 4m2 – 2m. Bring down 13. 2m – 1 Multiply 2m – 1 by 1. 14 Subtract 2m – 1; remainder is 14. 14ANSWER (13 + 4m ) ÷ (–1 + 2m) = 2m + 1 + 2 2m – 1
  16. 16. 9.4 Warm-Up (Day 1)Divide.1. − 3d 7 ÷ (−9d 4 )2. 8 z ÷ (−6 z 5 )3. (6 x 3 + 3 x 2 − 12 x) ÷ 3 x
  17. 17. 9.4 Warm-Up (Day 2)Divide.1. (a 2 + 3a − 4) ÷ (a − 1)2. (9b 2 + 6b + 8) ÷ (3b − 4)3. (8m − 7 + 4m 2 ) ÷ (5 + 2m)

×