Factoring Quadratics

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What is factoring in algebra?

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Factoring in algebra is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

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What is a quadratic expression?

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A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants and a ≠ 0.

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What are the common methods for factoring quadratics?

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Common methods for factoring quadratics include: 1) Factoring by grouping, 2) Using the quadratic formula, 3) Recognizing perfect squares, and 4) Applying the difference of squares.

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What is the difference of squares?

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The difference of squares is a factoring technique that applies to expressions of the form a² - b², which can be factored as (a - b)(a + b).

Tags

CCSS.HSA.APR.C.4

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How do you factor a quadratic expression in the form ax² + bx + c?

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To factor a quadratic expression in the form ax² + bx + c, look for two numbers that multiply to ac (the product of a and c) and add to b. Rewrite the expression using these numbers and factor by grouping.

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What is a perfect square trinomial?

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A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, typically in the form (a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b².

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CCSS.HSA.APR.C.4

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What is the factored form of x² - 9?

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The factored form of x² - 9 is (x - 3)(x + 3), which is an example of the difference of squares.

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CCSS.HSA.APR.C.4

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How do you factor the expression 5x² + 20x + 20?

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First, factor out the greatest common factor (GCF), which is 5, resulting in 5(x² + 4x + 4). Then, recognize that x² + 4x + 4 is a perfect square trinomial, which factors to 5(x + 2)².

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CCSS.HSA.APR.C.4

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What is the factored form of 25x² - 9?

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The factored form of 25x² - 9 is (5x - 3)(5x + 3), which is another example of the difference of squares.

Tags

CCSS.HSA.APR.C.4

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What is the significance of the quadratic formula?

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The quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), provides a method to find the roots of any quadratic equation, allowing for solutions even when factoring is difficult.

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