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# 9.4.1

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• End of day 1
• Day 2
• 1. d^3/3 2. -4/3z^4 3. 2x^2+x-4
• 1. a+4 2. 3b+6+32/3b-4 3. 2m-1+(-2)/2m+5
• ### 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)