Solving Polynomial Equations of HIGHER Degree Factor Polynomial
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![Solving Polynomial Equations of HIGHER Degree Solving Polynomial Equations of HIGHER Degree](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-2.jpg)
![Factor Polynomial Expressions The methods we learned can also be used to solve polynomial Factor Polynomial Expressions The methods we learned can also be used to solve polynomial](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-3.jpg)
![Solving Polynomial Equations The expressions on the previous slide are now equations: y= x Solving Polynomial Equations The expressions on the previous slide are now equations: y= x](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-4.jpg)
![Solve y = x 3 – 2 x 2 0 = x 2(x – Solve y = x 3 – 2 x 2 0 = x 2(x –](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-5.jpg)
![Solve Let y = 0 y = x 4 – x 3 – 3 Solve Let y = 0 y = x 4 – x 3 – 3](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-6.jpg)
![Using the Quadratic Formula Solve the following cubic equation: equation still need to solve Using the Quadratic Formula Solve the following cubic equation: equation still need to solve](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-7.jpg)
![Now… Solving Radical Expressions Now… Solving Radical Expressions](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-8.jpg)
![](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-9.jpg)
![A radical equation is an equation that contains a radical. A radical equation is an equation that contains a radical.](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-10.jpg)
![The goal in solving radical equations is the same as the goal in solving The goal in solving radical equations is the same as the goal in solving](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-11.jpg)
![We need to isolate the variable. We need to isolate the variable.](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-12.jpg)
![But there is only one way to move the variable out from under the But there is only one way to move the variable out from under the](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-13.jpg)
![We need to square the radical expression. We need to square the radical expression.](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-14.jpg)
![And, because it is an equation, what we do to one side, And, because it is an equation, what we do to one side,](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-15.jpg)
![And, because it is an equation, what we do to one side, we have And, because it is an equation, what we do to one side, we have](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-16.jpg)
![And now, we need to simplify: And now, we need to simplify:](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-17.jpg)
![Remember, no matter what n is. (Even if n is an expression) Remember, no matter what n is. (Even if n is an expression)](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-18.jpg)
![So we have: So we have:](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-19.jpg)
![Another Example: Another Example:](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-20.jpg)
![Solve for x: Step 1. Isolate the radical Solve for x: Step 1. Isolate the radical](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-21.jpg)
![Solve for x: Step 2. Square both sides. Solve for x: Step 2. Square both sides.](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-22.jpg)
![Solve for x: Step 3. Set one side equal to 0 Solve for x: Step 3. Set one side equal to 0](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-23.jpg)
![Solve for x: Step 4. Factor Solve for x: Step 4. Factor](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-24.jpg)
![Solve for x: Step 5. Solve the Equation x+3=0 x = -3 x– 1=0 Solve for x: Step 5. Solve the Equation x+3=0 x = -3 x– 1=0](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-25.jpg)
![Classwork: • Punchline 13. 13 • Factoring Summary Worksheet • Sheet 28 Classwork: • Punchline 13. 13 • Factoring Summary Worksheet • Sheet 28](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-26.jpg)
![Homework: Textbook Pg 24 – 25 Exercises: 87, 88, 89, 91, 92, 96, 97, Homework: Textbook Pg 24 – 25 Exercises: 87, 88, 89, 91, 92, 96, 97,](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-27.jpg)
- Slides: 27
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![Solving Polynomial Equations of HIGHER Degree Solving Polynomial Equations of HIGHER Degree](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-2.jpg)
Solving Polynomial Equations of HIGHER Degree
![Factor Polynomial Expressions The methods we learned can also be used to solve polynomial Factor Polynomial Expressions The methods we learned can also be used to solve polynomial](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-3.jpg)
Factor Polynomial Expressions The methods we learned can also be used to solve polynomial degree Commonequations of higher Grouping – take Factor common factor out of the first two terms and the last two terms. 2(x – 2) x – = x 4 – x 3 – 3 x 2 + 3 x = x(x 3 – x 2 – 3 x + 3) = x[x 2(x – 1) – 3(x – 1)] Comm 2 – 3)(x – 1) on x(x = Facto r x 3 2 x 2
![Solving Polynomial Equations The expressions on the previous slide are now equations y x Solving Polynomial Equations The expressions on the previous slide are now equations: y= x](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-4.jpg)
Solving Polynomial Equations The expressions on the previous slide are now equations: y= x 3 – 2 x 2 and y= x 4 – x 3 – 3 x 2 +3 x We will be solving for x when y = 0.
![Solve y x 3 2 x 2 0 x 2x Solve y = x 3 – 2 x 2 0 = x 2(x –](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-5.jpg)
Solve y = x 3 – 2 x 2 0 = x 2(x – 2) Let y = 0 Common factor Separate the factors and set them equal to zero. x 2 = 0 or x – 2 = 0 x=2 Solve for x Therefore, the solutions are 0 and 2.
![Solve Let y 0 y x 4 x 3 3 Solve Let y = 0 y = x 4 – x 3 – 3](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-6.jpg)
Solve Let y = 0 y = x 4 – x 3 – 3 x 2 + 3 x 0 = x(x 3 – x 2 – 3 x + 3) 0 =x[x 2(x – 1) – 3(x – 1)] 0 = x(x – 1)(x 2 – 3) Common factor Group Separate the factors and set them equal to zero. Solve for x x = 0 or x – 1 = 0 or x 2 – 3 = 0 x=1 x= Therefore, the solutions are 0, 1 and ± 1. 73
![Using the Quadratic Formula Solve the following cubic equation equation still need to solve Using the Quadratic Formula Solve the following cubic equation: equation still need to solve](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-7.jpg)
Using the Quadratic Formula Solve the following cubic equation: equation still need to solve for x y = x 3 + 5 x 2 – 9 x Can this. We be factored? here. Can this equation be 2 it can – – 9) 0 YES = x(x + 5 x factored? factor. xcommon =0 x 2 + 5 x – 9 = 0 are no two We. No. can, There however, use the quadratic formula. integers that will multiply a=1 to -9 and add to 5. Remember, the solution 0 came from an earlier step. b=5 c = -9 Therefore, the solutions are 0 and -5±√ 61 2
![Now Solving Radical Expressions Now… Solving Radical Expressions](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-8.jpg)
Now… Solving Radical Expressions
![](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-9.jpg)
![A radical equation is an equation that contains a radical A radical equation is an equation that contains a radical.](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-10.jpg)
A radical equation is an equation that contains a radical.
![The goal in solving radical equations is the same as the goal in solving The goal in solving radical equations is the same as the goal in solving](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-11.jpg)
The goal in solving radical equations is the same as the goal in solving most equations.
![We need to isolate the variable We need to isolate the variable.](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-12.jpg)
We need to isolate the variable.
![But there is only one way to move the variable out from under the But there is only one way to move the variable out from under the](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-13.jpg)
But there is only one way to move the variable out from under the square root sign.
![We need to square the radical expression We need to square the radical expression.](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-14.jpg)
We need to square the radical expression.
![And because it is an equation what we do to one side And, because it is an equation, what we do to one side,](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-15.jpg)
And, because it is an equation, what we do to one side,
![And because it is an equation what we do to one side we have And, because it is an equation, what we do to one side, we have](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-16.jpg)
And, because it is an equation, what we do to one side, we have to do to the other.
![And now we need to simplify And now, we need to simplify:](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-17.jpg)
And now, we need to simplify:
![Remember no matter what n is Even if n is an expression Remember, no matter what n is. (Even if n is an expression)](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-18.jpg)
Remember, no matter what n is. (Even if n is an expression)
![So we have So we have:](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-19.jpg)
So we have:
![Another Example Another Example:](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-20.jpg)
Another Example:
![Solve for x Step 1 Isolate the radical Solve for x: Step 1. Isolate the radical](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-21.jpg)
Solve for x: Step 1. Isolate the radical
![Solve for x Step 2 Square both sides Solve for x: Step 2. Square both sides.](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-22.jpg)
Solve for x: Step 2. Square both sides.
![Solve for x Step 3 Set one side equal to 0 Solve for x: Step 3. Set one side equal to 0](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-23.jpg)
Solve for x: Step 3. Set one side equal to 0
![Solve for x Step 4 Factor Solve for x: Step 4. Factor](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-24.jpg)
Solve for x: Step 4. Factor
![Solve for x Step 5 Solve the Equation x30 x 3 x 10 Solve for x: Step 5. Solve the Equation x+3=0 x = -3 x– 1=0](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-25.jpg)
Solve for x: Step 5. Solve the Equation x+3=0 x = -3 x– 1=0 x=1
![Classwork Punchline 13 13 Factoring Summary Worksheet Sheet 28 Classwork: • Punchline 13. 13 • Factoring Summary Worksheet • Sheet 28](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-26.jpg)
Classwork: • Punchline 13. 13 • Factoring Summary Worksheet • Sheet 28
![Homework Textbook Pg 24 25 Exercises 87 88 89 91 92 96 97 Homework: Textbook Pg 24 – 25 Exercises: 87, 88, 89, 91, 92, 96, 97,](https://slidetodoc.com/presentation_image_h2/a25ff2f6335ad5f5951144c48fcc8173/image-27.jpg)
Homework: Textbook Pg 24 – 25 Exercises: 87, 88, 89, 91, 92, 96, 97, 99, 102, 106, 109
Polynomial functions of higher degree
Polynomial functions of higher degree with modeling
Polynomial
Factoring higher degree polynomials
Third degree polynomial equation
Unit 5 homework 6 dividing polynomials
Finding the real roots of polynomial equations
Solving polynomial equations by factoring
Factor the expression. 4r2 – 64
Solving polynomial equations in factored form
5-3 solving polynomial equations
Factor x^3-125
Nth degree polynomial function
A polynomial of the form y=ax2+bx+c is called
Degree and leading coefficient
Degree of a monomial
Polynomial degree names
Whats a monomial
How to find the zeros of a function
Polynomial names by degree and number of terms
Naming polynomials by degree
Classify each polynomial by its degree and number of terms
Classification of polynomials
Even degree polynomial
Xaxxx
Review graphing polynomials
Polynomial terms
Polynomial function examples