Synthetic Division - WordPress.com
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Example: ( β + ) Γ· ( β ) BEGIN HOW β TO: SYNTHETIC DIVISION
Transcript of Synthetic Division - WordPress.com
Example: (πππ β ππ + π) Γ· (π β π)
BEGIN
HOW β TO: SYNTHETIC DIVISION
Example: (πππ β ππ + π) Γ· (π β π)
Step #1: Draw a corner and a baseline.
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Example: (πππ β ππ + π) Γ· (π β π)
Step #2: Look at the expression youβre dividing by. Put the OPPOSITE of the number sitting next to x in the corner.
5
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Example: (πππ β ππ + π) Γ· (π β π)
Step #3: Next to the corner, write the coefficients of each term of the first polynomial. Donβt forget placeholders!!!
5 4 0 -2 1
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π₯3 π₯2 π₯ π
Example: (πππ β ππ + π) Γ· (π β π)
Step #4: Drop down the first number outside of the corner below the baseline.
5 4 0 -2 1
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π₯3 π₯2 π₯ π
5 4
Example: (πππ β ππ + π) Γ· (π β π)
Step #5: Multiply the number in the corner by the number you just dropped down below the baseline. Write the result above the baseline in the next column.
5 4 0 -2 1
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π₯3 π₯2 π₯ π
x 4
5 4 20
Example: (πππ β ππ + π) Γ· (π β π)
Step #6: You should now have a column with two values. Add them together, and write the result below the baseline.
5 4 0 -2 1
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π₯3 π₯2 π₯ π
x 4 20
+5 4 20 +
Example: (πππ β ππ + π) Γ· (π β π)
Step #7: Multiply the number in the corner by the number you just added to the baseline. Put this above the baseline in the next column.
5 4 0 -2 1
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π₯3 π₯2 π₯ π
x 4 20
+5 4 20 100
Example: (πππ β ππ + π) Γ· (π β π)
Step #8: Repeat steps 6 & 7 until there are no empty spots below the baseline.
5 4 0 -2 1
NEXT
π₯3 π₯2 π₯ π
x 4 20 98
+5 4 20 100 +
Example: (πππ β ππ + π) Γ· (π β π)
Step #8: (Cont.) Repeat steps 6 & 7 until there are no empty spots below the baseline.
5 4 0 -2 1
NEXT
π₯3 π₯2 π₯ π
x 4 20 98
+5 4 20 100 490
Example: (πππ β ππ + π) Γ· (π β π)
Step #8: (Cont.) Repeat steps 6 & 7 until there are no empty spots below the baseline.
5 4 0 -2 1
NEXT
π₯3 π₯2 π₯ π
x 4 20 98 491
+5 4 20 100 490 +
Example: (πππ β ππ + π) Γ· (π β π)
Step #9: Each number on the baseline represents the coefficient of a variable with ONE LESS degree than the column started out with. The constantβs column gives the remainder.
5 4 0 -2 1
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π₯3 π₯2 π₯ π
x 4 20 98 491
+5 4 20 100 490
π₯2 π₯ π π
Example: (πππ β ππ + π) Γ· (π β π)
Step #10: Write out the result of the division.
5 4 0 -2 1 π₯3 π₯2 π₯ π
x 4 20 98 491
+5 4 20 100 490
π₯2 π₯ π π
= πππ + πππ + ππ +πππ
π β π
Try this one on your own!
πππ + ππ + π Γ· π + π
Donβt click βNextβ until youβve completed the problem!
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Example: πππ + ππ + π Γ· π + π
NEXT
Draw corner and baseline!
Example: πππ + ππ + π Γ· π + π
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-2
Look at the polynomial youβre dividing by. Put the OPPOSITE of the number sitting next to x in the corner.
Example: πππ + ππ + π Γ· π + π
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-2 3 7 2
Write the coefficients of the first polynomial!
π₯2 π₯ π
Example: πππ + ππ + π Γ· π + π
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-2 3 7 2
-2 3 Drop down the first number.
π₯2 π₯ π
Example: πππ + ππ + π Γ· π + π
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-2 3 7 2
-2 3
-2 -6
-2 β 3 = -6
π₯2 π₯ π
Example: πππ + ππ + π Γ· π + π
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-2 3 7 2
-2 3 1
-2 -6
7 + -6 = 1
π₯2 π₯ π
Example: πππ + ππ + π Γ· π + π
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-2 3 7 2
-2 3 1
-2 -6 -2
-2 β 1 = -2
π₯2 π₯ π
Example: πππ + ππ + π Γ· π + π
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-2 3 7 2
-2 3 1 0
-2 -6 -2
2 + -2 = 0
π₯2 π₯ π
Example: πππ + ππ + π Γ· π + π
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-2 3 7 2
-2 3 1 0
-2 -6 -2
Write what powers each coefficient now represents.
π₯2 π₯ π
π₯ π π
Example: πππ + ππ + π Γ· π + π
-2 3 7 2
-2 3 1 0
-2 -6 -2
Write final answer.
π₯2 π₯ π
π₯ π π
= ππ + π
