Mr. Sims
Algebra 1
Section 11.7 B
Dividing Polynomials
Divide.
1. (6x2 + 4x – 9) ÷ 3
6x 2 4x 9

 
3
3 3
2 4x
 2x   3
3
divide each term by 3
simplify
2. (12x3 – 4x2 – 3x + 6) ÷ (-x)
12x 3 4x 2 3x
6




divide each term by -x
x x x x
 12x 2  4x  3 
6
x
simplify
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3. (-6x3 + 8x2 – 3x – 9) ÷ (-2x)
 6x 3 8x 2
3x
9




 2x  2x  2x  2x
3 9
 3x  4x  
2 2x
2
divide each term by –2x
simplify
4. (-8x6 + 6x4 – 3x2 + 9) ÷ 2x2
 8x 6 6x 4 3x 2
9

 2  2  2 divide each term by 2x2
2
2x
2x
2x
2x
9
4
2 3
 4x  3x   2 simplify
2 2x
Mr. Sims
Use long division to divide the polynomials.
5. (x2 + 3x – 40) ÷ (x – 5)
x +8
x  5 x 2  3x  40
x2 – 5x
8x - 40
8x – 40
0
- divide 1st terms {x into x2}
- multiply back x(x – 5)
- subtract {watch signs}
- bring down the -40
- divide 1st terms {x into 8x}
- multiply back 8(x – 5)
- subtract {watch signs}
- no remainder
Mr. Sims
6. (6x2 + 13x + 8) ÷ (2x + 1)
3x + 5 + 3
2x + 1
2
2x  1 6x  13x  8 - divide 1st terms {2x into 6x2}
- multiply back 3x(2x + 1)
6x2 + 3x
- subtract
10x + 8
- bring down the 8
10x + 5
- divide 1st terms {2x into 10x}
3
- multiply back 5(2x + 1)
- subtract
- remainder is 3, put it
over 2x + 1
Mr. Sims
7. (5x2 – 3x + 7) ÷ (x – 1)
5x + 2 + 9
x-1
2
x  1 5x  3x  7
- divide 1st terms {x into 5x2}
- multiply back 5x(x – 1)
5x2 – 5x
- subtract {watch signs}
2x + 7
- bring down the 7
2x - 2
- divide 1st terms {x into 2x}
9
- multiply back 2(x – 1)
- subtract {watch signs}
- remainder is 9, put it
over x - 1
Mr. Sims
8. (x4 + 2x2 – 3x + 6) ÷ (x – 3)
missing an x3 term
fill in with 0x3
x3
+
3x2 +
96
11x + 30 + x - 3
x  3 x 4  0x 3  2x 2  3x  6
x4 – 3x3
3x3 + 2x2
3x3 – 9x2
11x2 - 3x
11x2 – 33x
- subtract {watch signs}
30x + 6
- remainder is 96, put it
30x - 90
over x - 3
96
- divide 1st terms {x into x4}
- multiply back x3(x – 3)
- subtract {watch signs}
- bring down the 2x2
- divide 1st terms {x into 3x3}
- multiply back 3x2(x – 3)
- subtract {watch signs}
- bring down the –3x
- divide 1st terms {x into 11x2}
- multiply back 11x(x – 3)
- subtract {watch signs}
- bring down the 6
- divide 1st terms {x into 30x}
- multiply back 30(x – 3)
Mr. Sims
Algebra 1
Section 11.7 B
Dividing Polynomials
Divide.
1.) (3x2 + 8x – 2) ÷ 2
2.) (7x2 + 5x – 2) ÷ x
3.) (x10 – 18) ÷ x
4.) (3x2 + 18x) ÷ 3x
5.) (6x2 – 4x + 5) ÷ 2x
6.) (16x3 + 8x2 – 4x + 2) ÷ 4x
7.) (13x + 4) ÷ (x – 2)
8.) (x2 – 8) ÷ (x – 2)
9.) (3x2 – 10x – 15) ÷ (x – 5)
10.) (9x – 8) ÷ (3x – 1)
11.) (10x2 + 4x + 7) ÷ (2x + 1)
Mr. Sims
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