real zeros of polynomials section 2.4. review – long division 1. what do i multiply by to get the...
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Real Zeros of Polynomials
Section 2.4
Review – Long Division
1. What do I multiply by to get the first term?
2. Multiply through
3. Subtract
4. Bring down next term
CONCLUSION
CONCLUSION
Review: Synthetic Division
1. Solve the divisor for “x”
2. Set up problem with coefficients ONLY
3. Bring down the first term
4. Multiply, add, repeat
FACTOR THEOREM
(x – k) is a factor of a polynomial if and only if f(k)
= 0
Practice Determine whether each binomial is a FACTOR
of f(x) = x3 + 3x2 – 6x – 8
1. (x – 2)
2. (x + 3)
3. (x + 4)
Rational Zeros Theorem
Rational #s – numbers that can be written as fractions
POSSIBLE rational zeros of a polynomial can
be found by dividing the factors of the LAST
TERM and LEADING COEFFICIENT
Practice – find possible rational zeros
f(x) = 3x3 + 4x2 – 5x – 2
Factors of -2:
Factors of 3:
1, -1, 2, -2
1, -1, 3, -3
1, -1, 2, -2
List all of the POSSIBLE rational zeros of
f(x) = 2x3 – x2 – 9x + 9
PUTTING IT ALL TOGETHER1. Find all of the zeros (rational & irrational)
f(x) = 2x3 – 3x2 – 4x + 6
Step 1: List possible rational zerosStep 2: Find one from the list that IS a zeroStep 3: Synthetic DivisionStep 4: Factor
Ticket Out1.) Is 2x + 1 a factor of 4x3 - 8x2 – 1 ? Show work
2.) Divide x3 – 5x2 + 3x – 2 by (x + 1) using LONG division
3.) Divide x3 – 5x2 + 3x – 2 by (x + 1) using SYNTHETIC
4.) List all possible rational zeros of f(x) = 2x4 + 3x – 3
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