6.3 Synthetic Division
Notes 6.3 ­ Dividing Polynomials
Long Division Demo: Let's divide for fun!
"Old School Arithmetic"
Yea...I knew there was an easier way to divide polynomials!
"Fancy Polynomial Dividing"
Let's learn a short cut for dividing polynomials!
And the crowd goes wild!!!
6.3 Synthetic Division
Synthetic Division Example 1
Ask ­ Is my dividend in standard form? Are all powers represented?
Ask ­ Is my divisor linear (x1 power) with a lead coefficient of 1?
Divide 2 x2 + 7 x + 7
2
7
7
Set divisor = 0
and solve for x.
Remainder
= Quotient + Synthetic Division Example 2
Ask ­ Is my dividend in standard form? Are all powers represented?
Ask ­ Is my divisor linear (x1 power) with a lead coefficient of 1?
2
Divide ­2 x4 + 3 x3 ­5 x
­2
3 ­5
­6÷ (x ­ 3)
Set divisor = 0
and solve for x.
Remainder
= Quotient + 6.3 Synthetic Division
Synthetic Division ­ Homework Prob #19
Ask ­ Is my dividend in standard form? Are all powers represented?
Ask ­ Is my divisor linear (x1 power) with a lead coefficient of 1?
Divide
Set divisor = 0
and solve for x.
Remainder
= Quotient + Synthetic Division ­ Homework Prob #20
Ask ­ Is my dividend in standard form? Are all powers represented?
Ask ­ Is my divisor linear (x1 power) with a lead coefficient of 1?
Divide
Set divisor = 0
and solve for x.
Remainder
= Quotient + 6.3 Synthetic Division
Synthetic Division Template
Divide (Ax4 + Bx3 + Cx2 + Dx + E)
Dividend
By (x­k)
Divisor (Note x must have a coefficient = 1)
Put coefficients of the terms of the dividend in the top row outside of a backward "L". Make sure the dividend is in descending order with all powers represented.
Set the divisor equal to 0 and solve for x. Put this value inside the backward "L."
"K" is a multiplier
Values under the line represent coefficients of the quotient
K A B C D E
A
Remainder is at the end.
Step 1: Drop A value below the line.
Step 2: Multiply A by K and put result under B
Step 3: Add B with the value underneath and put below the line.
Step 4: Multiply the sum in step 3 by K and put under C.
Step 5: Repeat multiplication and addition until last sum is under E.
Dividend/Divisor = Quotient + Remainder/Divisor
Assignment: Section 6.3
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