Writing and solving equations of polynomials
Presentation
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Medium
KATIE KENNEDY
Used 11+ times
FREE Resource
5 Slides • 13 Questions
1
Solving Polynomials
By KATIE KENNEDY
2
Quadratics are Polynomials
Quadratics are the polynomials you have the most experience with. Many of the things that are true of quadratics are true of polynomials.
1. In order to solve quadratics, we must set the equation equal to zero.
2. We use the zero product property to solve when the equation has been factored to find the solutions.
3. The solutions (also called zeros) correspond to the x-intercepts of the graph of the equation.
4. We can use the graph to determine an equation.
What's good for the goose...
3
Quadratics are Polynomials
Any property or process completed on a quadratic, can be used to solve polynomials as well!
...Is good for the gander
4
Fill in the Blanks
Type answer...
5
Multiple Choice
If a polynomial is written in factored form, what do you need to do to find an x value?
Nothing, the factors are the variable's values
Set the factors equal to zero and solve for the variable
Set them equal to each other and solve for the variable
Multiply them all together and isolate the variable to find its value
6
Math Response
If a polynomial contains the factor (x-5), then it will have a solution of _____. (just the number)
7
Fill in the Blanks
Type answer...
8
Drag and Drop
0=(5x+3)(2x−1)(x−2)
{
9
Drag and Drop
0=10x2−9x−9
{
10
Drag and Drop
0=x4+27x
{
11
Drag and Drop
0=4x3−64x
{
12
Drag and Drop
x4−16x2=64−4x2
{
13
Writing Polynomial Equations
By KATIE KENNEDY
14
Equations from graphs
To write an equation form a graph, you must follow the steps:
1. Find the zeros on the graph (these are the x intercepts).
2. Write them in x= form (EX: x=n)
3. Find the factor by solving so that you have an equation equal to zero (EX: x-n=0 gives you the factor (x-n))
4. Write the polynomial as a product of its factors. Write the equation equal to zero.
Hint: Write factors in order of the zeros left to right so you don't miss any!!!!!
x=-3
x+3=0
(x+3)
x=0
(x)
x=5
x-5=0
(x-5)
Polynomial equation:
0=x(x+3)(x-5)
15
Math Response
Write the equation from the graph of the polynomial:
(make sure it is set equal to zero)
16
Math Response
Write the equation from the graph of the polynomial:
(Make sure it is set equal to zero)
17
Math Response
When the graph bounces off the axis at the zero, the degree of the corresponding factor is even (2).
The factor corresponding to 1 is a squared factor: (x-1)2
Write the equation from the graph of the polynomial:
(Make sure it is set equal to zero)
18
Math Response
When the graph bounces off the axis at the zero, the degree of the corresponding factor is even (2).
The factor corresponding to 1 is a squared factor: (x-1)2
Write the equation from the graph of the polynomial:
(Make sure it is set equal to zero)
Solving Polynomials
By KATIE KENNEDY
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