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Transcript
Homework #4
Pre Calculus
Due 9/30/08
Name:
1.
Period
Date:
Factor the following quadratics
(a)
p( x)  x 2  x  30
(b)
p ( x)  4 x 2  5 x  6
How did you decide which numbers to try as factors? Did you use the Factor Theorem? How would you extend your
thinking in 1 to factor higher order polynomials?
2.
f ( x)  x 4  3x3  15x 2  19 x  30 . If we were to factor this polynomial as
( x  a)( x  b)( x  c)( x  d ) , what would be the possible values of a, b, c and d?
Given the polynomial
Try to find the values of a, b, c, and d by using the Factor Theorem and dividing out each factor as you successfully find
it.
Graph the function on your calculator to check your answers.
3.
The polynomial equation 3x  5 x  26 x  8  0 has a solution which is not an integer, but it is a rational number. To
use your calculator to help you find the solutions in such a case, set the xscl to 1/3. (Why would we do this?) Set the
window to:
Xmin = -5
Ymin = -20
Xmax = 5
Ymax = 60
Xscl = 1/3
Yscl = 1
3
2
If we look at the graph we see that it crosses the x-axis one notch to the right at x 
twelve notches to the left at
4.
1
, six notches to the right at x  2 ,
3
x  4 . Write this equation in factored form and show that the factoring works.
Use a similar technique to solve 2 x  x  31x  15  0 (what is your x-step here?)
3
2
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5.
Use the rational roots theorem and the factor theorem to factor the following polynomials (you may use your calculator as
much as you like)
(a) x  3x  4 x  12
4
2
(b) 2 x  5 x  14 x  5 x  12
4
6.
3
2
Use the Remainder Theorem to solve the following.
p ( x)  x 3  x 2  x  5 .
Find p (7)
(a) Given
(b) Given g  x   3x
3
 12 x 2  9 x  1
Find g ( 5)
7. What would the remainder be if 2 x134  7 x 45  x9  4 is divided by ( x  1) ?
8.
Factor the following polynomials into products of linear and quadratic factors. Then, solve the equations. Your solutions
may be complex numbers.
(a) x  1  0
3
(b) x  16  0
4
9.
Factor the following polynomials. For each one, note the kinds of zeros (complex, real, rational, irrational, or integer).
(a)
p ( x)  x 4  2 x 2  1
(b)
s ( x)  x 3  3x 2  3x  2
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