Download 3-4 factoring polynomials

Chapter 3
3-4 factoring polynomials
Objectives
Use the Factor Theorem to determine
factors of a polynomial.
Factor the sum and difference of two
cubes.
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.
Factor theorem
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)
Example#2
 Determine
whether the given binomial is a
factor of the polynomial P(x).
 a.
(x + 2); (4x2 – 2x + 5)
Student guided practice
 Do
problems 1-3 in your book page 177
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.
Factoring by Grouping
 Factor:
x3 – x2 – 25x + 25.
 Factor: 2x3 + x2 + 8x + 4.
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.
Factoring the Sum or
Difference of Two Cubes
 Factor
the expression.
 4x4 + 108x
 125d3 – 8
Student guided practice
 Do
problems 4-8 in your book page 176
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).
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).
Homework
 Do
odd problems from 17-32 in your book
page 177
closure
 Today
we learned about polynomials
 Next class we are going to learned about
finding real roots in polynomials