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)

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Divide
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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.

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Divide using polynomial long division
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Divide using synthetic division
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Divide
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Divide
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Divide
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5.5 Given polynomial f(x) and a factor of f(x),
factor f(x) completely.
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Academy Algebra II

• 5.5 FINISH Polynomial Long Division
• and Synthetic Division
• Hw 5.5 p.366 (8, 22, 28, 30, 32, 36)

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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.

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Given polynomial f(x) and a factor of f(x),
factor f(x) completely.
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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.

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Given polynomial f(x) and a zero of f(x), find
the other zeros.
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Given polynomial f(x) and a zero of f(x), find
the other zeros.
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Given polynomial f(x) and a factor of f(x),
factor f(x) completely.
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Given polynomial f(x) and a zero of f(x), find
the other zeros.
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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)

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List all possible rational zeros using the
rational zero theorem.

• Every rational zero of a function has the
  following form

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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
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List all possible rational zeros using the
rational zero theorem.
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List all possible rational zeros using the
rational zero theorem.
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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.

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Find all real zeros of the function.
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Do Now Find all real zeros of the function.
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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)

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Find all real zeros of the function.
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Find all real zeros of the function.
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Do Now Find all real zeros of the function.