chapter 3 3-4 factoring polynomials. objectives use the factor theorem to determine factors of a...
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Chapter 3 3-4 factoring polynomials
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Objectives Use the Factor Theorem to determine
factors of a polynomial.Factor the sum and difference of two
cubes.
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Factor Theorem Recall that if a number is divided by any
of its factors, the remainder is 0. Likewise, if a polynomial is divided by any of its factors, the remainder is 0.
The Remainder Theorem states that if a polynomial is divided by (x – a), the remainder is the value of the function at a. So, if (x – a) is a factor of P(x), then P(a) = 0.
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Factor theorem
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Example#1 Determine whether the given
binomial is a factor of the polynomial P(x).
A. (x + 1); (x2 – 3x + 1) B. (x + 2);
(3x4 + 6x3 – 5x – 10)
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Example#2 Determine whether the given
binomial is a factor of the polynomial P(x).
a. (x + 2); (4x2 – 2x + 5)
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Student guided practice Do problems 1-3 in your book page 177
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Factoring You are already familiar with methods
for factoring quadratic expressions. You can factor polynomials of higher degrees using many of the same methods you learned.
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Factoring by Grouping
Factor: x3 – x2 – 25x + 25. Factor: 2x3 + x2 + 8x + 4.
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Factoring polynomials Just as there is a special rule for
factoring the difference of two squares, there are special rules for factoring the sum or difference of two cubes.
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Factoring the Sum or Difference of Two Cubes Factor the expression. 4x4 + 108x 125d3 – 8
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Student guided practice Do problems 4-8 in your book page 176
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Geometry Application
The volume of a plastic storage box is modeled by the function V(x) = x3 + 6x2 + 3x – 10. Identify the values of x for which V(x) = 0, then use the graph to factor V(x).
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Geometry application The volume of a rectangular prism
is modeled by the function V(x) = x3 – 8x2 + 19x – 12, which is graphed below. Identify the values of x for which V(x) = 0, then use the graph to factor V(x).
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Homework Do odd problems from 17-32 in your
book page 177
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closure Today we learned about polynomials Next class we are going to learned
about finding real roots in polynomials