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Bottom’s Up 4 Possibilities
Helpful Hint! Pay close attention to the positive and negative signs!
Possibility #1: ax² + bx +c (x + west) ( x + east) Larger # + Smaller # + + +
Examples of ax²+bx +c Every problem we did yesterday for homework!
Possibility #2: ax² - bx + c (x – west) (x- east) + - Larger # - Smaller # -
Examples of ax² - bx + c 1.) x² – 6x ) a² -14a ) 6 -13x + 6x² 4.) 15x² – 19x + 6
Possibility #3: ax² + bx - c (x + west) (x- east) - Larger # + Smaller # - +
Examples of ax² + bx - c 1.) x² + x – 42 2.) x² + 6xy -72y² 3.) 5x² + x ) 24x⁴ + 47x² -2
Possibility #4: ax² - bx - c (x- west) (x + east) - Larger # - Smaller # + -
Examples of ax² –bx -c 1.) x² -7x ) y²–xy -2x² 3.) 2x² -7x -4 4.) 2x² – x - 1
X Factor: 4 Options Smaller # - + Larger # Smaller # + Larger # -
Homework Worksheet #2
Bottom’s Up 4 Possibilities. X Factor: 4 Options Smaller # - + Larger # Smaller # + Larger # -
Factoring ax 2 +bx +c ax 2 +bx +c a is the coefficient of the squared term or the term with a degree of 2. b is the coefficient of the middle term or the.
FACTORING Think Distributive property backwards Work down, Show all steps ax + ay = a(x + y)
Factoring by Grouping. When you have 4 terms Remember– To factor out a GCF, we write the GCF on the outside and divide each term by the GCF. Ex) x 5 y.
EXAMPLE 1 Factor when b is negative and c is positive Factor 2x 2 – 7x + 3. SOLUTION Because b is negative and c is positive, both factors of c must be.
MULT. INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.
9-6 X-box Factoring ax 2 +bx+c. X-box Factoring This is a guaranteed method for factoring quadratic equations—no guessing necessary! We will learn how.
Ch. 5.4: Factoring (PART 1). GCF: Pull common term out from all terms Ex: Pull out 2x Pull out 3 Pull out 6xy.
Factor P (8-5ab) 2. 4(d² + 4) 3. 3rs(2r – s) 4. 15cd(1 + 2cd) 5. 8(4a² + 3b²) 6. 12xy(3y – 4x) 7. 5x²y(6x + 7y) 8. 3cd²(3c² - 2d) 9. 15bc³(5b +
FACTORING Think unfoil Work down, Show all steps ax 2 + bx + c.
DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.
6.4 and 6.5 Factoring Trinomials “Using Bottom’s Up Method”
Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the parabola opens up, the lowest point is called the.
8-3 Factoring x 2 + bx + c Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.
Do Now 4/15/10 Take out HW from yesterday. Practice worksheet 10.2 form B odds Practice worksheet 10.2 form B odds Copy HW in your planner. Text p.
EXAMPLE 1 Factor trinomials of the form x 2 + bx + c Factor the expression. a. x 2 – 9x + 20 b. x 2 + 3x – 12 SOLUTION a. You want x 2 – 9x + 20 = (x.
SUBTRACTING INTEGERS 1. CHANGE THE SUBTRACTION SIGN TO ADDITION 2. TAKE THE INVERSE OF THE SECOND NUMBER 3. FOLLOW THE RULES FOR ADDITION 4. ADD THE OPPOSITE.
For Educational Use Only © Factoring ax 2 + bx + c Brian Preston Algebra
5.2 Properties of Parabolas 1.Graphing Parabolas 2.Finding Maximum and Minimum Values.
Factoring Patterns There is a pattern for factoring trinomials of this form, when c is positive x² + bx + c.
FACTORING REVIEW EXAMPLES 1. Factor x 2 + 3x – 4Solve x 2 + 3x – 4 = 0 Graph Y 1 = x 2 + 3x – 4 Find x-intercepts What _____× _____ = – 4 and _____+ _____.
What two numbers will give you a product of 64 and a quotient of 4?
MULTIPLICATION EQUATIONS 1. SOLVE FOR X 3. WHAT EVER YOU DO TO ONE SIDE YOU HAVE TO DO TO THE OTHER 2. DIVIDE BY THE NUMBER IN FRONT OF THE VARIABLE.
Do Now 3/3/10 Take out HW from last night. Text p. 578, #4-48 multiples of 4 Copy HW in your planner. Text p. 586, #4-52 multiples of 4 In your notebook,
Holt Algebra Factoring ax 2 + bx + c 8-4 Factoring ax 2 + bx + c Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz.
Factoring Quadratic Equations Objective: To factor a quadratic expression and to use factoring to solve quadratic equations.
Example 2. The length of a rectangle is 7 more than the width. Its area is 30. Find the dimensions of the rectangle. x x + 7 A = 30 A = lw 30 = x(x + 7)
For Educational Use Only © Factoring x 2 + bx + c Brian Preston Algebra
Factor each trinomial: x 2 + 4x + 3 (x + 3)(x + 1)
AN INTRESTING FACT If A B C D E F G H I J K L M N O P Q R S T U V W X Y Z is equal to
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