```College Algebra: Lesson 5.1 Introduction to Polynomial Equations and Graphs
1. A polynomial function can be written in the form p( x)  a n x n  a n 1 x n 1  ....  a1 x  a 0 , where n is a whole
number.
2. The largest power of a polynomial is called the degree of the polynomial.
3. A coefficient is the number in front of the variable, and the leading coefficient is the number in front of the
biggest power of x.
4. A solution of an equation is a value that makes the equation true when it is substituted into the equation.
5. To solve a quadratic equation, you can solve by factoring or use the quadratic formula. x 
 b  b 2  4ac
2a
You can determine the "end behavior" of a graph by looking at the degree and leading coefficient.
1. If the degree is even:
2. If the degree is odd:
Examples
Consider the following polynomial.
a. Determine the degree and the leading coefficient of r(x).
b. Describe the behavior of the graph of r(x) as x   .
r ( x)   ..as...x   and r ( x)   ..as...x  
1. r ( x)  8 x 2  8x  2
2. r ( x)  6 x 5  4 x 3  7 x 2  10  32
3. Does the given value of x solve the polynomial equation?
 59 x 2  3x  6 x 3  80; x  10
3. r ( x)  6 x 2 ( x  5)( x  1)
4. Solve the polynomial equation by factoring or using the quadratic formula, making sure to identify all the
solutions.
a. x 2  9 x  44  0
b. x 3  20 x  9 x 2
a. ( x  4)( x  3)( 2  x)  0
b. x( x  5)( x  4)  0
c. x 2   x  20
d. x( x  5) 2 ( x  8)  0
e. 4 x 2  x  3
f. 3x 3  2 x 2  1
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6. Determine the x-intercepts, the y-intercept and the correct graph of the polynomial function. Enter all points
as ordered pairs, separate multiple answers with a comma, and select the graph from the options below.
a. s( x)  ( x  2)( x  1)(5  x)
b. f ( x)  x 2  x  2
c. r ( x)  ( x  2)( x  1)( x  1)( x  2)
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