Solve by Factoring

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What is the process of solving a quadratic equation by factoring?

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Factoring involves rewriting the quadratic equation in the form (ax + b)(cx + d) = 0, then setting each factor to zero to find the values of x.

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What is a quadratic equation?

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What are the roots of a quadratic equation?

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1. Factor the quadratic: (x + 11)(x + 4) = 0. 2. Set each factor to zero: x + 11 = 0 or x + 4 = 0. 3. Solve for x: x = -11 or x = -4.

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What is the zero product property?

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Factor out the common term: 7x(x - 4) = 0. Set each factor to zero: 7x = 0 or x - 4 = 0. Solutions are x = 0 and x = 4.

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What is the significance of the leading coefficient in a quadratic equation?

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The leading coefficient (a) determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.