2.3. Long and Synthetic Division.notebook
October 18, 2013
2.3. Finding Real Zeroes of Polynomial functions. LONG DIVISION and SYNTHETIC
DIVISION.
EXAMPLE:
Given f(x) = x3­2x2­7x+2 find all zeroes of f(x) and write the equation in complete factored form. EXAMPLE:
Given f(x) = x3­2x2­7x+2 , find all real zeroes of f(x) and write the equation in complete factored form. We know that there will be
Using table feature of yor calculator you found f(­2) = 0 .
What is the definition of a factor??
is divisible by
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2.3. Long and Synthetic Division.notebook
October 18, 2013
LONG DIVISION
completely factored
rational
irrational
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2.3. Long and Synthetic Division.notebook
October 18, 2013
EXAMPLE:
Given f(x) = 2x3+3x2­8x+3 and f(1) = 0 , find all real zeroes of f(x) and write the equation in complete factored form. EXAMPLE:
Given f(x) = 10x3­15x2­16x+12 and f(2) = 0 , find all real zeroes of f(x) and write the equation in complete factored form. 3
2.3. Long and Synthetic Division.notebook
October 18, 2013
EXAMPLE:
Given f(x) = 6x3­19x2+16x­4 and f(2) = 0 , find all real zeroes of f(x) and write the equation in complete factored form. Long Division vs. Synthetic Division
Given f(x) = 6x3­19x2+16x­4 and f(2) = 0 , find all real zeroes of f(x) and write the equation in complete factored form. There is a nice shortcut for long division of polynomials when dividing by the divisors of the form x – k. It is called synthetic division. *Synthetic division works ONLY for divisors of the form x – k. We cannot use synthetic division to divide a polynomial by a quadratic like x² + 3. To divide a polynomial by x – k, use the following pattern:
Vertical pattern: ADD terms
Diagonal pattern: Multiply by k
divide by a ZERO
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2.3. Long and Synthetic Division.notebook
October 18, 2013
LONG DIVISION AND SYNTHETIC DIVISION PRACTICE:
Divide by we expected no remaider
since the original expression
was factorable.
Divide by 5
2.3. Long and Synthetic Division.notebook
October 18, 2013
OTL: Page 123/ 3, 5, 13, 15, 19, 21
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