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Algebra II Recipe: Solving Quadratic Equations by Factoring
A. Factoring using the GCF
  1. Find the largest number common to every coefficient or number.
  2. Find the GCF of each variable.
    • It will always be the variable raised to the smallest exponent.
  3. Find the terms that the GCF would be multiplied by to equal the original polynomial.
ExamplesExamples:
3x² - 6x
2x² - 4x + 8
5x²y³ + 10x³y
B. Factoring the Difference of Two Squares
  1. The factors will always be (a + b)(a - b).
  2. The "a" and "b" represent terms.
ExamplesExamples:
9x² - 49
121x² - 100
25x² - 64y²
C. Factoring a Perfect Square Trinomial
  1. Characteristics
    • "ax²" term is a perfect square.
    • "c" term is a perfect square.
    • "c" term is positive.
    • Factors into two identical binomials: (a + b)2.
  2. Steps to Factor
ExamplesExamples:
9x² - 30x + 25
4x² + 28xy + 49y²
2x² + 16x + 32
16x³ + 80x² + 100x
D. Factoring Using the 6-Step Method to Factor ax² + bx + c
  1. Multiply "a" and "c".
  2. Find two numbers that multiply to equal this product, but adds to equal "b".
    • When a = 1 stop here. The two numbers chosen will be the numbers in the two binomial factors
  3. Use these two numbers to rewrite the "x" term when writing out the problem again.
    • When you have a choice, write the negative term first.
  4. Group the first two terms and the last two terms together.
    • If the third term from the left has subtraction in front, add the opposite before grouping.
  5. Factor the GCF out of each set of parentheses.
    • If you added the opposite in step 4, factor a negative GCF out of the second set of parentheses.
  6. The two GCFs make up one binomial factor and the common set of parentheses is the other binomial factor.
ExamplesExamples:
2x² - 7x - 4
x² + 6x - 16
2x² + 7x + 5
6x² - 13x + 5
E. Steps to Solving Quadratic Equations Using Factoring
  1. Set all terms equal to zero.
  2. Factor the quadratic completely.
  3. Set each factor having a variable equal to zero.
  4. Solve each equation.
  5. If we were to graph the quadratic equation, these values would be the x-intercepts. The numbers you get are the solutions.
ExamplesExamples:
2x² + 3x = 5
4x² + 2x = 0
3x² + 7x + 2 = 0
12x² - 5x - 3 = 0




G Redden

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