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Copy of Solving Quadratic Equations by Factoring

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jeff marquez

on 4 October 2013

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Transcript of Copy of Solving Quadratic Equations by Factoring

Notes
Ideas
Ideas
Ideas
Solving Quadratic Equations by Factoring
Objectives
Solve quadratic equations by factoring
State, illustrate, and apply the zero – product property of real numbers in solving quadratic equations.
InfoMath
Although in Latin the prefix "quadri" means four, the word "quadrus" means a square (because it has four sides) and "quadratus" means "squared." Consider other words such as: "quadrille," meaning a square dance; "quadrature," meaning constructing a square of a certain area.

Quadratic equations were originally used in connection with geometric problems involving squares. Since the second power is called a "square," equations with the highest power being two are called quadratic equations.
Let's Do this!
Group yourself into four groups. Each group will complete the following table using the given expressions.
Evaluation:
Solve for the roots of the following quadratic equations
1. x exp 2 + 3x – 40 = 0
2. a exp 2 + 10a + 21 = 0
3. 8x exp 2 – 2x = 3
4. 8x exp 2 – 57x + 54 = 0

Generalization
 In solving for the roots of quadratic equation, we simply factor the trinomial and square each binomial factor to zero to obtain the value of the unknown variable or roots of the quadratic equations.
 Factoring as a tool in solving equations is limited, as you might have noticed. It can only be used in those quadratic equations where the quantity ax2 + bx + c is factorable.
Demonstration Lesson
The National Teachers Colleges The School of Advanced Studies Teaching in Mathematics
Definition: quadratic equations by factoring are normally expressed as where a does not equal zero.

Mathematical Ideas
Information
Types of Special products Polynomials Factors
Difference of two squares
Common Monomial Factor
Perfect Square Trinomial
Quadratic Trinomial

1. 3x exp 2 – 5x +2 (2x + 3)exp 2
2. X exp 2 – 25 x( x – 9)
3. X exp 2 – 9x (x + 5)(x – 5)
4. 4x exp 2 + 12x + 9 (3x -2) (x – 1)

Zero – Product Property of Real Numbers.
If a and b are real numbers, then ab = 0 if and only if a = 0 or b = 0.
To solve a quadratic equation by factoring:
1. Start with the equation in the standard form. Be sure it is set equal to zero!
2. Factor the left hand side (assuming zero is on the right)
3. Set each factor equal to zero
4. Solve to determine the roots (the values of x)

Factoring with DOTS
(difference of two squares)
Or Isolate the Variable
(Square Root Property)
Factoring with GCF
(greatest common factor)
Find the largest value that can be factored from each of the elements of the expression.
Factoring Trinomials
In a quadratic equation in descending order with a leading coefficient of one, look for the product of the roots to be the constant tern and the sum of the roots to be the coefficient of the middle term.
Factoring Harder Trinomials
If the leading coefficient is not equal to 1, you must think more carefully about how to set up your factors.
Tricky One!!
Be sure to get the equation set equal to zero before you factor.
More Examples
The factors of x exp 2 + 3x - 4 are:
(x+4) and (x-1)
Why? Well, let us multiply them to see:
(x+4)(x-1) = x(x-1) + 4(x-1)
= x exp 2 - x + 4x - 4
= x exp 2 + 3x - 4
Multiplying (x+4)(x-1) together is called Expanding.

Example: 6x exp 2 + 5x - 6
Example: 2x exp 2 + 7x + 3
Assignment:
Solve for the roots of the following quadratic equations
1. x exp 2 + 5x + 6 = 0
2. x exp 2 – 4x + 77 = 0
3. x exp 2 – 49 = 0
4. 9x exp 2 = 144

Group 4
"Best Group"
Full transcript