#3 Factoring Quadratics

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What is factoring in algebra?

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Factoring 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.

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What are the steps to factor a quadratic expression?

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1. Identify the coefficients a, b, and c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the middle term using these two numbers. 4. Factor by grouping.

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What does it mean to factor completely?

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Factoring completely means breaking down an expression into its simplest factors, including any common factors and irreducible polynomials.

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What is the difference between factoring and expanding an expression?

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Factoring involves rewriting an expression as a product of its factors, while expanding involves multiplying out the factors to obtain the original expression.

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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 a quadratic equation when factoring is difficult.

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What are the factors of a quadratic expression?

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The factors of a quadratic expression are the binomials that multiply together to yield the original quadratic expression.

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How do you factor a quadratic expression when a = 1?

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When a = 1, you look for two numbers that multiply to c and add to b, then write the expression as (x + m)(x + n), where m and n are the two numbers.

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What is the role of the discriminant in factoring quadratics?

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The discriminant, b² - 4ac, determines the nature of the roots of a quadratic equation: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

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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, such as (a + b)² = a² + 2ab + b².