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Sunday, 24 March 2013

Intermediate Algebra chapter 5 part 4

Synthetic Division
Chapter 5, 

When Synthetic Division Can Be Used
Use synthetic division only when the divisor has the form x - a, where a is some number.
How to Do Synthetic Division--Learn by Example
Dividend must be written in descending powers of x.
Divisor must have the form x - a.


Problem:  Divide  
x3 + x + 10
x + 2


Write coefficients of dividend on the first line.
Notice the 0 for 0x2, which is a missing power of x.
Write in a of x - a.
Notice x + 2 = x - (-2).
Carry 1 down.
-2 = -2 · 1.
Add 0 and -2 to get -2.
4 = -2 · -2.
Add 1 and 4 to get 5.
-10 = -2 · 5.
Add 10 and -10 to get 0.
Completed synthetic division.
Quotient is 1x2 + (-2)x + 5.
Remainder is 0.


Notes
x3 + x + 10 = (x + 2)(x2 - 2x + 5)
Notice that when the remainder is 0, the divisor and quotient are factors of the dividend, as the above equation shows.
Dividendx3 + x + 10
Divisorx + 2
Quotientx2 - 2x + 5
Remainder0
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