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

October 19, 2015
Obj: To learn about Long Division of Polynomials, Remainder and Factor
Theorems, Synthetic Division, Rational Zeros Theorem.
Synthetic Division
3
2
Divide 2x - 3x - 5x - 12 by x - 3 using synthetic division.
October 19, 2015
Obj: To learn about Long Division of Polynomials, Remainder and Factor
Theorems, Synthetic Division, Rational Zeros Theorem.
Rational Zeros Theorem:
If there are rational zeros in the polynomial:
f(x) = a x + an
xn
+ ...n+ -a1
then they will be in the set
n - 1
p
q
where p = factors of the constant, a
and
0
q = factors of the leading term coefficient, a
0
October 19, 2015
Obj: To learn about Long Division of Polynomials, Remainder and Factor
Theorems, Synthetic Division, Rational Zeros Theorem.
Find the rational zeros of
f(x) = 3x3 + 4x2 - 5x - 2
October 19, 2015
Obj: To learn about Long Division of Polynomials, Remainder and Factor
Theorems, Synthetic Division, Rational Zeros Theorem.
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 19, 2015
Obj: To learn about Long Division of Polynomials, Remainder and Factor
Theorems, Synthetic Division, Rational Zeros Theorem.
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 19, 2015
Obj: To learn about Long Division of Polynomials, Remainder and Factor
Theorems, Synthetic Division, Rational Zeros Theorem.
Find the zeros.
f(x) = x4 - x3 - 2x -4
October 19, 2015
Find the zeros.
Obj: To learn about Long Division of Polynomials, Remainder and Factor
Theorems, Synthetic Division, Rational Zeros Theorem.
f(x) = 2x4 - 7x3 - 8x2 + 14x + 8
October 19, 2015
Obj: To learn about Long Division of Polynomials, Remainder and Factor
Theorems, Synthetic Division, Rational Zeros Theorem.
HW
(2.4)
(HR) Pg.205: 2, 3, 7, 11, 13, 15, 19, 21, 27, 33, 35, 37, 41, 49, 51, 53