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Academy Algebra II

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Academy Algebra II 5.5: Polynomial Long Division and Synthetic Division HW: 5.4: p.357 (30-40 even, 46-54 even) Divide Polynomial Long Division vs. Synthetic Division ... – PowerPoint PPT presentation

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Title: Academy Algebra II


1
Academy Algebra II
  • 5.5 Polynomial Long Division
  • and Synthetic Division
  • HW 5.4 p.357 (30-40 even, 46-54 even)

2
Divide
3
Polynomial Long Division vs. Synthetic Division
  • Polynomial Long Division can be used for any two
    polynomials.
  • Synthetic Division the divisor has to be in the
    form x k, where k is any constant.

4
Divide using polynomial long division
5
Divide using synthetic division
6
Divide
7
Divide
8
Divide
9
5.5 Given polynomial f(x) and a factor of f(x),
factor f(x) completely.
10
Academy Algebra II
  • 5.5 FINISH Polynomial Long Division
  • and Synthetic Division
  • Hw 5.5 p.366 (8, 22, 28, 30, 32, 36)

11
Given polynomial f(x) and a factor of f(x),
factor f(x) completely.
  • Steps
  • 1.) Divide the polynomial and the factor.
  • 2.) Factor the answer.
  • 3.) Write out all factors.

12
Given polynomial f(x) and a factor of f(x),
factor f(x) completely.
13
Given polynomial f(x) and a zero of f(x), find
the other zeros.
  • Zeros answers to the polynomial equation f(x)
    0.
  • Process.
  • 1.) Use the zero to factor the polynomial
    completely.
  • 2.) Solve to find the other zeros.

14
Given polynomial f(x) and a zero of f(x), find
the other zeros.
15
Given polynomial f(x) and a zero of f(x), find
the other zeros.
16
Given polynomial f(x) and a factor of f(x),
factor f(x) completely.
17
Given polynomial f(x) and a zero of f(x), find
the other zeros.
18
Academy Algebra II
  • 5.6 Find Rational Zeros
  • HW tonight p.374 (4-10 even)
  • Tomorrow p.374 (14-20 even)
  • Next day p.374-375 (24-30 even)

19
List all possible rational zeros using the
rational zero theorem.
  • Every rational zero of a function has the
    following form

20
List all possible rational zeros using the
rational zero theorem.
  • Example List the possible rational zeros for the
    function

Factors of the constant Factors of
the leading coefficient
Possible rational zeros
Possible rational zeros
21
List all possible rational zeros using the
rational zero theorem.
22
List all possible rational zeros using the
rational zero theorem.
23
Find the zeros of a polynomial function.
  • List the possible rational zeros of the function.
  • Test the zeros using division. (Since the zeros
    are x-intercepts, when you divide you should end
    up with a remainder of zero.)
  • Graph the function in the calculator to narrow
    your list. Only check reasonable values from the
    list.
  • The number of zeros is the same as the degree of
    the polynomial.

24
Find all real zeros of the function.
25
Do Now Find all real zeros of the function.
26
Academy Algebra II
  • 5.6 Find Rational Zeros
  • HW tonight p.374 (16-26 even)
  • Quiz Friday 5.5, 5.6
  • (Calculator and no calculator section)

27
Find all real zeros of the function.
28
Find all real zeros of the function.
29
Do Now Find all real zeros of the function.
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