Download Dividing a polynomial by a monomial

EQ: How do I divide a polynomial by a polynomial or a monomial?
Dividing a polynomial by a
monomial
Dividing a polynomial by a polynomial
LONG DIVISION
Notes #_______________
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
Step 2: Ask yourself, “What multiplied by (the first term in the
box. FILL IN ZEROS (place holders) FOR MISSING
divisor) gives me (the first term in the dividend)?”
TERMS!!
Step 3: Bring down the first term below the line
Step 3: Multiply your answer by each term of the divisor.
Step 4: Multiply what’s below the line by the number
outside. Put you answer under the next number
Step 4: Change all the signs and combine terms
inside the box.
2 4
4 5
a b a b
Step 5: Combine.
Step 5: Repeat 2 – 4 until you get a remainder.
4
Step 6: Repeat steps 3 – 5 until done.
ab
Step 7: YOUR ANSWER: The numbers under the
line are the coefficients of the quotient. Start with the
x 3 3x 2  3x  2
power of x that is one less than the degree of the
1.
dividend.
x 2 x  1
***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.
Divide each
individual term by
the monomial on
the bottom:
1.
ab 3 
Step 1: Fill in any zeros (place holders) for missing terms!!
1. (5x3 – 13x2 + 10x – 8)  (x – 2)
xy 2  x 4 y 5
2.
xy 4
x 4  x 2 3x  5
2.
x2  2
3. (3xy3 + 4xy –
5xy3) (xy) -1
2. (x3 – 4x2)  (x – 4)
********************************************
3. (8x4 – 4x2 + x + 4)  (2x + 1)
EQ: How do I divide a polynomial by a polynomial or a monomial?
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.
Notes #_______________
EQ: How do I divide a polynomial by a polynomial or a monomial?
Notes #_______________
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)