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MTH 092

MTH 092. Section 11.6 Solving Quadratic Equations By Factoring. Overview. This section utilizes the factoring techniques discussed in previous sections: --Greatest Common Factor (11.1) --Trinomials of the form ax 2 + bx + c (11.2, 11.3, 11.4)

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MTH 092

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  1. MTH 092 Section 11.6 Solving Quadratic Equations By Factoring

  2. Overview • This section utilizes the factoring techniques discussed in previous sections: --Greatest Common Factor (11.1) --Trinomials of the form ax2 + bx + c (11.2, 11.3, 11.4) --Difference of squares and perfect square trinomials (11.5)

  3. The Zero-Factor Property • What it says: if a and b are real numbers and ab = 0, then a = 0 or b = 0. • What it means: if the product of two numbers is 0, then at least one of the numbers must be 0. • How it applies: when we factor a polynomial, the result of our work is a product.

  4. Steps In The Process • Write the equation in standard form (all terms on the left in descending order, 0 on the right). • Factor completely. • Set each variable factor equal to 0. • Solve the resulting equations by isolating the variable. • Write your solutions in solution set form.

  5. Examples • (x + 3)(x + 2) = 0 • x(x – 7) = 0 • (9x + 1)(4x – 3) = 0 • x2 + 2x – 63 = 0 • x2 + 15x = 0 • (x + 3)(x + 8) = x • 4y3 – 36y = 0

  6. More Examples • 4y2 – 81 = 0 • 9x2 + 7x = 2 • (y – 5)(y – 2) = 28 • 9y = 6y2 • 4x2 – 20x = -5x2 – 6x – 5

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