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Bottom’s Up 4 Possibilities
X Factor: 4 Options Smaller # - + Larger # Smaller # + Larger # -
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
Bottom’s Up 4 Possibilities. Helpful Hint! Pay close attention to the positive and negative signs!
FACTORING Think Distributive property backwards Work down, Show all steps ax + ay = a(x + y)
FACTORING Think unfoil Work down, Show all steps ax 2 + bx + c.
MULT. INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.
DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.
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 +
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.
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.
Addition 1’s to
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.
Addition Facts = = =
25 seconds left….. 24 seconds left….. 23 seconds left…..
8-3 Factoring x 2 + bx + c Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.
Revision Algebra II Factorisation of Binomials, Trinomials, Sum & Difference of Two Cubics By I Porter.
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.
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.
27 9 =. 6 6 = 36 9 = 9 9 = 45 9 = 54 9 = =
6.4 and 6.5 Factoring Trinomials “Using Bottom’s Up Method”
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,
MULTIPLYING MONOMIALS TIMES POLYNOMIALS (DISTRIBUTIVE PROPERTY)
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ALGEBRAIC EXPRESSIONS Step 1 Write down the question Step 2 Plug in the numbers Step 3 Use PEMDAS Work down, Show all steps.
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For Educational Use Only © Factoring ax 2 + bx + c Brian Preston Algebra
Around the World AdditionSubtraction MultiplicationDivision AdditionSubtraction MultiplicationDivision.
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.
Positive and Negative Numbers. Do Now Solve. 1. x + 4 = y – 2.3 = z = = 8 x = 15 y = 10.1 z = 30 Course 2 w9w9 w = 72 Hwk: p 39.
2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4pt 5 pt 1pt Two-step linear equations Variables.
We will resume in: 25 Minutes We will resume in: 24 Minutes.
Frigid Fridays On each Friday last January, the temperature was a record low temperature for the date. On Friday, January 30, the mercury dropped to 5°F,
Mr. Coon’s Math Class. The answer to a multiplication problem. 6 X 6 = 36.
ADDING INTEGERS 1. POS. + POS. = POS. 2. NEG. + NEG. = NEG. 3. POS. + NEG. OR NEG. + POS. SUBTRACT TAKE SIGN OF BIGGER ABSOLUTE VALUE.
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Multiply Binomials (ax + b)(cx +d) (ax + by)(cx +dy)
Ch. 5.4: Factoring (PART 1). GCF: Pull common term out from all terms Ex: Pull out 2x Pull out 3 Pull out 6xy.
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Factor each trinomial: x 2 + 4x + 3 (x + 3)(x + 1)
1 Topic Factoring Quadratics ax ² + bx + c Factoring Quadratics ax ² + bx + c.
We need a common denominator to add these fractions.
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.
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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.
Factoring Patterns There is a pattern for factoring trinomials of this form, when c is positive x² + bx + c.
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)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Digital Lessons on Factoring.
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