6-3: DIVIDING POLYNOMIALS Essential Question: What does the last number in the bottom line of synthetic division represent?
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6-3: DIVIDING POLYNOMIALSEssential Question: What does the last number in the bottom line of synthetic division represent?
6-3: DIVIDING POLYNOMIALS
Using Long Division Polynomial Long division works similarly to
regular long division (I know… it’s been a while) Divide 1,732,042 by 440
3936440 1732042
1320
4120
3960
1604
1320
2842
2640
202
Answer is 3936, R: 202
6-3: DIVIDING POLYNOMIALS
Divide x2 + 3x – 12 by x – 3
2
2
6
6 1
3 3 12
6 12
6
8
3
x
x x
x x x
x
x
Answer is x + 6, R: 6
6-3: DIVIDING POLYNOMIALS
YOUR TURN Divide x2 – 3x + 1 by x – 4
2
2
4 3 1
1
4
1
5
4
x
x
x
x x
x
x
x
Answer is x + 1, R: 5
6-3: DIVIDING POLYNOMIALS We can use division to find factors of a
polynomial. If the remainder of division comes out to be 0, then
the divisor (and quotient) are factors. Determine whether x + 4 is a factor of the
polynomial x2 + 6x + 8.
Because the remainder is 0, x + 4 IS a factor of x2 + 6x + 8 (so is x + 2)
2
2 4
4 6 8
2
2
0
2 8
8
x x
x
x
x
x
x
x
6-3: DIVIDING POLYNOMIALS
Determine whether x + 4 is a factor of the polynomial x3 + 3x2 – 6x – 7.
Because the remainder is not 0, x + 4 IS NOT a factor of x3 + 3x2 – 6x – 7
3 2
2
2
2
3 2
4 3 6 7
6
4
2
2
1
8
4
2
7
x x
x x x x
x
x x
x x
x
x
x
6-3: DIVIDING POLYNOMIALS YOUR TURN Determine whether x – 8 is a factor of the
polynomial 2x2 – 19x + 24.
Because the remainder is 0, x – 8 IS a factor of 2x2 – 19x + 24
2
2
2
2 16
8 2 19 24
3 24
0
3
3 24
x x x
x
x
x
x
x
6-3: DIVIDING POLYNOMIALS YOUR TURN Determine whether x + 2 is a factor of the
polynomial x3 – 4x2 + 3x +2.
Because the remainder is not 0, x + 2 IS NOT a factor of x3 – 4x2 + 3x + 2
2
2
3
2
3
2
2
6
6 12
15
15 30
2 4 3 2
6 3
2
15 2
28
x x
x x x x
x
x
x
x
x
x
x
x
6-3: DIVIDING POLYNOMIALS
Assignment Page 324 Problems 1 – 12 (all problems) Obviously, show your work
Tomorrow Quiz review
Next week The secrets of synthetic division Chapter 6 Test
UNIT #4: POLYNOMIALS6-3: DIVIDING POLYNOMIALSDAY 2Essential Question: What does the last number in the bottom line of synthetic division represent?
6-3: DIVIDING POLYNOMIALS Synthetic Division
Can only be used when the divisor is “x” +/- some constant (e.g. “x + 2”, “x – 10”)
Step 1: Reverse the sign of the constant terms in the divisor. Write the coefficients of the polynomial in standard form.
Step 2: Bring down the first coefficient Step 3: Multiply the first coefficient by the new
divisor. Write the result under the next coefficient. Add.
Step 4: Repeat the steps of multiplying and adding until the remainder is found.
Step 5: The quotient begins one degree less than the dividend.
6-3: DIVIDING POLYNOMIALS
Divide 3x3 – 4x2 + 2x – 1 by x + 13 21 3 4 2 1x x x x
1 3 4 2 1
6-3: DIVIDING POLYNOMIALS
Divide 3x3 – 4x2 + 2x – 1 by x + 13 21 3 4 2 1x x x x
1 3 4 2 1
3
6-3: DIVIDING POLYNOMIALS
Divide 3x3 – 4x2 + 2x – 1 by x + 13 21 3 4 2 1x x x x
1 3 4 2 1
3
3 7
6-3: DIVIDING POLYNOMIALS
Divide 3x3 – 4x2 + 2x – 1 by x + 13 21 3 4 2 1x x x x
1 3 4 2 1
3 7
3 7 9
6-3: DIVIDING POLYNOMIALS
Divide 3x3 – 4x2 + 2x – 1 by x + 1
The quotient is 3x2 – 7x + 9, R: -10
3 21 3 4 2 1x x x x
1 3 4 2 1
3 7 9
3 7 9 10
6-3: DIVIDING POLYNOMIALS
YOUR TURN Divide x3 – 4x2 + x – 6 by x – 3
Answer is x2 – 1x – 2, R: -12
3 1 4 1 6
3 3 6
1 1 2 12
6-3: DIVIDING POLYNOMIALS
Assignment Page 324 – 325 Problems 13 – 22 & 48 – 51 (all problems) Obviously, show your work
Tomorrow Chapter 6 Review Packet will be distributed
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