Download Divide 2x3 - 3x2 - 5x - 12 by x

October 14, 2011
Synthetic Division
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Divide 2x - 3x - 5x - 12 by x - 3 using synthetic division.
October 14, 2011
Rational Zeros Theorem:
If there are rational zeros in the polynomial:
f(x) = anxn + an-1xn-1 + ... + a0
then they will be in the set
p
q
where p = factors of the constant, a0
and
q = factors of the leading term coefficient, an
October 14, 2011
Find the rational zeros of
f(x) = 3x3 + 4x2 - 5x - 2
October 14, 2011
Upper and Lower Bound Tests for Real Zeros
Suppose f(x) is divided by x - k using synthetic division.
1. If k≥ 0 and every number in the last line is nonnegative (pos. or
zero), then k is an upper bound for the real zeros of f.
2. If k ≤ 0 and the numbers in the last line alternate nonnegative
and nonpositive, then k is a lower bound for the real zeros of f.
October 14, 2011
Prove that k = 5 is an upper bound for the real
zeros of f(x) = 2x3 - 5x2 - 5x - 1
Prove that k = -4 is a lower bound for the real
zeros of f(x) = 3x3 - x2 - 5x - 3
October 14, 2011