Factoring Quadratics

Front

What is factoring in mathematics?

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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.

Front

What is a quadratic expression?

Back

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

Front

What does it mean to factor a quadratic expression completely?

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Factoring a quadratic expression completely means expressing it as a product of its linear factors, if possible, and ensuring that no further factoring is possible.

Front

What is the standard form of a quadratic equation?

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The standard form of a quadratic equation is ax² + bx + c = 0, where a ≠ 0.

Front

What is the quadratic formula?

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The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

How do you identify the coefficients in a quadratic expression?

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In the expression ax² + bx + c, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

What is the significance of the discriminant in a quadratic equation?

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

Front

What is the first step in factoring a quadratic expression?

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The first step in factoring a quadratic expression is to look for two numbers that multiply to 'ac' (the product of the coefficient of x² and the constant term) and add to 'b' (the coefficient of x).

Front

What is the factored form of the expression 3v² - 4v - 7?

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(3v - 7)(v + 1) is the factored form of 3v² - 4v - 7.

Front

What is the factored form of the expression 5x² - 7x + 2?

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(5x - 2)(x - 1) is the factored form of 5x² - 7x + 2.