Notes Day 4 ­ Possible Rational Roots Theorem.notebook
December 05, 2014
Mini­Polynomial Unit
Day 4
Synthetic Division, Remainder Theorem, Rational Root Theorem & Solving Equations
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Notes Day 4 ­ Possible Rational Roots Theorem.notebook
December 05, 2014
Factor using long division. (x2 ­ 3x ­ 21) (x ­ 7)
(­5x2 + x3 + 8x + 4) (­1 + x)
2
Notes Day 4 ­ Possible Rational Roots Theorem.notebook
December 05, 2014
Use synthetic division to find q(x) and r(x). x3 ­ 13x2 + 40x + 18
x ­ 7
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Notes Day 4 ­ Possible Rational Roots Theorem.notebook
December 05, 2014
Use the Remainder Theorem to find the remainder.
Is the binomial a factor of the polynomial? (10x3 ­ 11x2 ­ 47x + 30) (x ­ 2)
(2x4 + 14x3 ­ 2x2 ­ 14x) (x + 7)
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Notes Day 4 ­ Possible Rational Roots Theorem.notebook
December 05, 2014
Possible Rational Root Theorem
f(x) = anxn + an­1xn­1 + ... + a1x + a0 =
where an 0 and a
0
=
0
The factors of an are the "q"s
The factors of a0 are the "p"s
+ p
q are the possible rational roots
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Notes Day 4 ­ Possible Rational Roots Theorem.notebook
December 05, 2014
Use the Rational Root Theorem to list all possible rational roots. f(x) = 3x2 + 2x ­ 1
f(x) = x3 ­ 27
f(x) = 5x4 + 32x2 ­ 21
6
Notes Day 4 ­ Possible Rational Roots Theorem.notebook
December 05, 2014
Find all zeros by:
a) using the Rational Root Theorem
b) locating probable roots using a graph
c) using synthetic division to reduce a quadratic
d) solve the quadratic
f(x) = x3 + 4x2 + 5x +2
f(x) = 4x3 ­ 9x2 + 6x ­ 1
f(x) = x4 ­ x3 + 14x2 ­ 16x ­ 32
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