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5.2 Polynomials, Linear Factors, and Zeros

5.2 Polynomials, Linear Factors, and Zeros . P288-292. Ex) Write the polynomial in factored form. The following statements are equivalent: (x-b) is a linear factor of P(x) b is a zero of y=P(x) b is a of P(x)=0 b is a solution of P(x)=0 b is an x-intercept of y=P(x).

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5.2 Polynomials, Linear Factors, and Zeros

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  1. 5.2 Polynomials, Linear Factors, and Zeros P288-292

  2. Ex) Write the polynomial in factored form.

  3. The following statements are equivalent: • (x-b) is a linear factor of P(x) • b is a zero of y=P(x) • b is a of P(x)=0 • b is a solution of P(x)=0 • b is an x-intercept of y=P(x)

  4. Ex) Find the zeros of the function. Then graph.

  5. Factor Theorem: x-a is a factor of P(x) if and only if the value of a is a zero of y=P(x)

  6. Ex) Write a polynomial function in standard form with the given zeros: a) -2, 2, and 3.

  7. Ex) Write a polynomial function in standard form with the given zeros: b) -2, -2, 2 and 3.

  8. Repeated linear factors are called multiple zeros. a is a zero of multiplicity n means that (x-a) appears n times as a factor.

  9. Ex) Find the zeros. State the multiplicity of multiple zeros.

  10. Ex) Find the relative maximum and relative minimum of the graph.

  11. Ex) Find the relative maximum and relative minimum of the graph.

  12. Ex) The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 times the height, what should each dimension be? Height = x Length = 1.5x 6 = 1.5x + width + x  width = 6 – 2.5x Volume = (x)(1.5x)(6-2.5x)

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