Writing and solving equations of polynomials

Solving Polynomials

By KATIE KENNEDY

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...

Quadratics are Polynomials

Any property or process completed on a quadratic, can be used to solve polynomials as well!

...Is good for the gander

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

Math Response

If a polynomial contains the factor (x-5), then it will have a solution of _____. (just the number)

Type answer here

Correct Answer: 5

Deg^°

Rad

Drag and Drop

List the solutions in set notation for the polynomial below.



$$0=\left(5x+3\right)\left(2x-1\right)\left(x-2\right)$$

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List the solutions in set notation for the polynomial below.



$$0=10x^2-9x-9$$

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List the solutions in set notation for the polynomial below.



$$0=x^4+27x$$

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List the solutions in set notation for the polynomial below.



$$0=4x^3-64x$$

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List the solutions in set notation for the polynomial below.



$$x^4-16x^2=64-4x^2$$

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Writing Polynomial Equations

By KATIE KENNEDY

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)

Math Response

Write the equation from the graph of the polynomial:

(make sure it is set equal to zero)

Type answer here

Correct Answer: 0=\left(x+8\right)\left(3x-2\right)\left(x-10\right)

Deg^°

Rad

Math Response

Write the equation from the graph of the polynomial:

(Make sure it is set equal to zero)

Type answer here

Correct Answer: 0=\left(x+8\right)\left(x+3\right)\left(x-3\right)

Deg^°

Rad

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)

Type answer here

Correct Answer: 0=x\left(x-1\right)^2\left(x-3\right)^2

Deg^°

Rad

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)

Type answer here

Correct Answer: 0=\left(x+5\right)\left(x+2\right)^2\left(x-1\right)\left(x-2\right)^2

Deg^°

Rad