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Bell Ringer
In elementary school, you learned long division. Describe, in detail, how to divide 232 by 4 without a calculator.
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Dividing Polynomials
Tuesday, September 16, 2014
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Long DivisionFor Polynomials
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Divide a Polynomial by a Monomial
The 1st way may be what you are used to seeing. The 2nd way is written like a rational function. Just like fractions, we can split it up. Then we can follow the rules of exponents.
6xy2 - 3xy + 2x2y
xy xy xy
6y -3 + 2x
Ex: (6xy2 – 3xy + 2x2y)
÷xy
Is the same as:
6xy2 – 3xy + 2x2yxy
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You Try
(5ab2 – 4ab + 7a2b) (ab)-1
Hint – First make the negative exponent positive.
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Divide a Polynomial by a Binomial
Just like in elementary school…
Divide Multiply Subtract Bring Down If there is a
remainder… write it as a fraction.
Like with decimals, you may need a placeholder.
Ex: 1. (x2 – 10x – 24 ) ÷ (x
+ 2)
2. (8x4 – 4x2 + x +4) ÷ (2x + 1)
3. (x3 + y3) ÷ (x + y)
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You Try 1. (3a4 – 6a3 – 2a2 + a – 6) ÷ (a +
1)
2. (t2 + 3t – 9) ÷ (5 – t ) Hint: reorder the denominator
3. (3x3 – 5x2 + 10x – 3) ÷ (3x + 1)
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Synthetic DivisionFor Polynomials
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Divide a Polynomial by a Binomial
You can only use synthetic division when dividing by a binomial that is of degree 1 with a coefficient of 1.
IF the coefficient is not 1, you can divide the polynomial and binomial by the coefficient and then use synthetic division, but it’s messy, so you might as well use long division.
Ex: 1. (5x3 – 13x2 + 10x – 8) ÷ (x – 2)
2. (x3 + 13x2 – 12x – 8) ÷ (x + 2)
1. Write the coefficients.
2. Put the opposite of the constant of the divisor in the box.
3. Bring down, multiply, add, repeat.
4. Write your answer (1 degree less than the dividend).
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You Try
1. (b4 – 2b3 + b2 – 3b + 2) ÷ (b – 2)
2. (x2 – 4x + 6) ÷ (x – 3)
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ClassworkAlgebra II book p. 236-237 #16-54 even
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HomeworkPolynomial Division Worksheet
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Exit Ticket1. By a show of hands, who prefers synthetic division?2. Why?