INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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### Dividing Polynomials

• To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.
• To divide a trinomial by a binomial, try to factor the trinomial. If you can, then cancel any common binomial factors in the divisor and the dividend.
• If there is no common binomial factor, or if the degree of the dividend is greater than 2, then use long division.
• When dividing a polynomial by a binomial using long division, any terms missing in the dividend must be written explicitly, using a coefficient of 0.

### Dividing Polynomials

Divide:
[(12x2 − 4x + 10x − 6)/2x]
• [(12x3)/2x] − [(4x2)/2x] + [10x/2x] − [6/2x]
6x2 − 2x + 5 − [3/x]
Divide:
[(25y4 + 60y3 − 75y)/5y]
5y3 + 12y2 − 15 − [1/y]
Divide:
[(54m4 + 60m2 − 48m + 24)/6m]
9m3 + 10m − 8 + [4/m]
Divide:
[(2n2 + 3n − 20)/(n + 4)]
• [(( n + 4 )( 2n − 5 ))/(n + 4)]
2n − 5
Divide:
[(3n2 − n − 24)/(n − 3)]
• [(( 3n + 8 )( n − 3 ))/(n − 3)]
3n + 8
Divide:
[(( 5j2 + 14 )( j + 2 ))/(j + 2)]
5j + 4
Divide: [(6p2 + 17p − 10)/(3p + 10)]
• [(( 3p + 10 )( 2p − 1 ))/(3p + 10)]
2p − 1
Divide:
[(( 4x3 − 10x2 + 12x − 8 ))/(( x − 2 ))]
• [((4x3−10x2 +12x−8))/((x−2))]
•  4x2
 x−2
 )
 4x3
 −10x2
 +12x
 −8
 −(4x3
 −8x2)
 −2x2
•  4x2
 x−2
 )
 4x3
 −10x2
 +12x
 −8
 −(4x3
 −8x2)
 −2x2
 +12x
 −(2x2
 +4x)
 8x
•  4x2
 x−2
 )
 4x3
 −10x2
 +12x
 −8
 −(4x3
 −8x2)
 −2x2
 +12x
 −(2x2
 +4x)
 8x
 −8
 −(8x
 −16)
 8
• (x−2)(4x2−2x+8)+8
• 4x3 −2x2+8x−8x2+4x−16+8
4x3−10x2+12x−8
Divide:
[(( 5y3 + 35y − 10y + 65 ))/(( y + 5 ))]
•  y+5
 )
 5y3
 35y2
 −10y
 +65
•  5y2
 y+5
 )
 5y3
 35y2
 −10y
 +65
 −(5y3
 +25y2)
 10y2
•  5y2
 +10y
 y+5
 )
 5y3
 35y2
 −10y
 +65
 −(5y3
 +25y2)
 10y2
 −10y
 −(10y2
 +50y)
 −60y
•  5y2
 +10y
 −60
 y+5
 )
 5y3
 35y2
 −10y
 +65
 −(5y3
 +25y2)
 10y2
 −10y
 −(10y2
 +50y)
 −60y
 +65
 −(−60y
 −300)
 365
• (y+5)(5y2+10y−60)+365
• 5y3+10y2−60y+25y2+50y−300+365
5y3+35y2−10y+65
Divide:
[((6a2+12a2−11a+3))/(a+1)]
•  6a2
 3a+1
 )
 6a2
 12a2
 −11a
 +3
 −(6a3
 +6a2)
 6a2
•  6a2
 −2a
 3a+1
 )
 6a2
 12a2
 −11a
 +3
 −(6a3
 +6a2)
 6a2
 −(−6a2
 −2a)
 −9a
•  6a2
 −2a
 −3
 3a+1
 )
 6a2
 12a2
 −11a
 +3
 −(6a3
 +6a2)
 6a2
 −(−6a2
 −2a)
 −9a
 −(−9a
 −3)
 6
• (3a+1)(6a2−2a−3)+6
• 18a3−6a2−9a+6a2−2a−3+6
18a3−11a+3

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Dividing Polynomials

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Dividing a Polynomial by a Monomial 0:11
• Example: Regular Fractions
• Example: Polynomials
• Dividing a Polynomial by a Binomial 2:56
• Example: Dividend and Divisor
• Long Division 5:28
• Example: Regular Numbers
• Example: Polynomials
• Missing Terms 12:20
• Definition
• Example
• Example 1: Divide the Polynomials 18:42
• Example 2: Divide the Polynomials 20:54
• Example 3: Divide the Polynomials 23:28
• Example 4: Divide the Polynomials 28:52