Pre calculus
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Pre-Calculus. Unit 7: Lesson 2: Polynomial Equations. Warm-Up. Study your notes. There will be a 5 question timed quiz and an exit ticket at the end of the period today. Topic/Objective:. I will learn how to find all possible solutions, rational or irrational. Essential Question:.

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Pre-Calculus

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Pre calculus

Pre-Calculus

Unit 7: Lesson 2:

Polynomial Equations


Warm up

Warm-Up

Study your notes.

There will be a 5 question timed quiz and an exit ticket at the end of the period today.


Topic objective

Topic/Objective:

I will learn how to find all possible solutions, rational or irrational.


Essential question

Essential Question:

How do find all zeros in a polynomial equation?


Notes

Notes:

Terminology Background:

  • Real Roots:

    • Physical x-intercepts

    • Factors that are real numbers

    • Numbers are rational

  • Complex Roots:

    • May not cross the x-axis

    • Might have imaginary numbers

    • Might have irrational or rational numbers


Notes1

Notes:

Terminology Continued:

  • Rational Numbers:

    • Exact numbers

  • Irrational Numbers:

    • Non-exact and exact numbers

    • Could contain imaginary values


Notes2

Notes:

Terminology Continued:

  • Double Roots:

    • A root that appears twice in a solution of an algebraic equation.

  • Depressed Polynomial:

    • A sad polynomial (just kidding)

    • Actually: New polynomial after dividing an original one by something.


Pre calculus

Finding Solutions:

The Zero Product Rule:

“If (A)(B)(C)=0, then either A = 0, B = 0, or C = 0”

Example:

(x + 8)(x – 1)(2x – 7) = 0

x + 8 = 0x – 1 = 02x – 7 = 0

x = -8x = 1x = 7/2= 3.5


Pre calculus

Finding Irrational Solutions:

You have done this in Algebra by using the….

Quadratic Formula:

For the quadratic function ax2 + bx + c = 0 then:


Your assignment

Your Assignment:

Complete “Polynomial Equation” worksheets.

If you do not finish them then it is homework.

Quiz: Last ten minutes of class.


Quiz time

Quiz Time!


Exit ticket

Exit Ticket:

  • Write at least three questions in the left hand column.

  • Summarize your notes by following the “Summary Paragraph Template” at your tables.


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