Chapter 6-3 Dividing Polynomials (std Alg 2 3.0)

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Chapter 6-3 Dividing Polynomials (std Alg 2 3.0)

• Objectives
• To understand long division of polynomials
• To understand synthetic division of polynomials
• To understand the Remainder Theorem and the
  Factor Theorem

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Zeros of a Polynomial Function

• If P is a polynomial and c is a real number, then
  the following are true.
• c is a zero of P.
• x c is a solution of the equation P(x) 0.
• x c is a factor of P(x).
• x c is an x-intercept of the graph of P.

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Ex 1. Factor
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Ex 2. Find the zeros by factoring and ZPP

• P(x) x3 3x2 10x

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Ex 3. Divide by x 4.
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Ex 4. Use synthetic division to divide
by
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Class Work

• Divide.
• 1.
  
• 2.

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Remainder Theroem

• If the polynomial P(x) is divided by x c, then
  the remainder is the value P(c).

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Ex 5. Use synthetic division and the Remainder
Theorem to evaluate P(c).
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Factor Theroem

• c is a zero of P if and only if
• x c is a factor of P(x).

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Ex 6. Use the Factor Theorem to show that x c
is a factor of P(x) for the given value of c and
find all other zeros of P(x).
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Class Work

• 3. Use synthetic division and the Remainder
  Theorem to evaluate P(c).
• 4. Use the Factor Theorem to show that x c is a
  factor of P(x) for the given value of c and find
  all other zeros of P(x).

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Ex 7. Find a polynomial of the specified degree
that has the given zeros.

• degree 3 zeros -3, 0, and 1
• Degree 3 zeros 1, 3, and 4