EQ: How do I divide a polynomial by a polynomial or a monomial?Notes #______

Dividing a polynomial by a monomial / Dividing a polynomial by a polynomial
LONG DIVISION / Dividing a polynomial by a binomial whose degree is 1
SYNTHETIC DIVISION
Divide each individual term by the monomial on the bottom:
1.


2.

3. (3xy3 + 4xy – 5xy3) (xy) -1 / Step 1: Fill in any zeros (place holders) for missing terms!!
Step 2: Ask yourself, “What multiplied by (the first term in the divisor) gives me (the first term in the dividend)?”
Step 3: Multiply your answer by each term of the divisor.
Step 4: Change all the signs and combine terms

Step 5: Repeat 2 – 4 until you get a remainder.

1.







2.


/ Step 1: Set the binomial = 0 and solve. Put this number outside the upside down box.
Step 2: Put the coefficients into the upside down box. FILL IN ZEROS (place holders) FOR MISSING TERMS!!
Step 3: Bring down the first term below the line
Step 4: Multiply what’s below the line by the number outside. Put you answer under the next number inside the box.
Step 5: Combine.
Step 6: Repeat steps 3 – 5 until done.
Step 7: YOUR ANSWER: The numbers under the line are the coefficients of the quotient. Start with the power of x that is one less than the degree of the dividend.
***Step 8: (only when the divisor has a leading coefficient other than 1) – you must divide all terms by the l.c. of the divisor.
  1. (5x3 – 13x2 + 10x – 8) (x – 2)







2. (x3 – 4x2) (x – 4)



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  1. (8x4 – 4x2 + x + 4) (2x + 1)

Dividing a polynomial by a monomial

1)Separate the fraction into as many terms as the numerator.

2)Divide using the rules of monomial division.

Examples:

1.

2.

3.

Dividing a polynomial by a binomial whose degree is 1

SYNTHETIC DIVISION

Step 1: Set the binomial = 0 and solve. Put this number outside the upside down box.

Step 2: Put the coefficients into the upside down box. FILL IN ZEROS (place holders) FOR MISSING TERMS!!

Step 3: Bring down the first term below the line

Step 4: Multiply what’s below the line by the number outside. Put you answer under the next number inside the box.
Step 5: Combine the columns in the box.

Step 6: Repeat steps 3 – 5 until done.

Step 7: YOUR ANSWER: The numbers under the line are the coefficients of the quotient. Start with the power of x that is one less than the degree of the dividend.

***** When the divisor has a leading coefficient other than 1, you must divide all terms of your answer by the leading coefficient! ******

  1. (8x3 – 10x2 + 3x – 5) (x + 4)2. (x3 – 6x2) (x – 7)

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3. (6x4 – 3x2 + x + 2) (3x + 2) 4. (4x3+3x+5) (2x +1)