4.2 Warm Up (what factoring method)

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What is the Difference of Perfect Squares method in factoring?

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The Difference of Perfect Squares method is used to factor expressions of the form a^2 - b^2, which can be factored as (a - b)(a + b).

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How do you identify a quadratic expression suitable for X-Factor method?

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A quadratic expression is suitable for the X-Factor method if it can be expressed in the form ax^2 + bx + c, where a, b, and c are constants.

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What is the GCF (Greatest Common Factor) method in factoring?

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The GCF method involves factoring out the largest factor common to all terms in an expression.

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What types of expressions can be factored using the Difference of Perfect Squares method?

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Expressions that can be factored using this method are those that can be written as the difference between two perfect squares, such as x^2 - 9 or x^2 - 1.

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What does it mean if an expression is 'Not Factorable'?

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An expression is 'Not Factorable' if it cannot be expressed as a product of simpler expressions, often because it does not have rational roots.

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What is the first step in factoring a quadratic expression using the X-Factor method?

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The first step is to identify two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x).

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Can the expression x^2 - 2 be factored? If so, how?

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The expression x^2 - 2 cannot be factored over the integers, as it does not have rational roots.

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What is the general form of a quadratic expression?

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The general form of a quadratic expression is ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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What is the significance of the coefficients in a quadratic expression when using the X-Factor method?

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The coefficients determine the roots of the quadratic equation and are essential for finding the factors.

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How can you check if your factored expression is correct?

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You can check by multiplying the factors back together to see if you obtain the original expression.