Factoring Quadratic Expressions

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 and a ≠ 0.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of two binomials, such as (x + p)(x + q), where p and q are numbers that satisfy the equation.

Front

What is the standard form of a quadratic expression?

Back

The standard form of a quadratic expression is ax² + bx + c, where a, b, and c are real numbers.

Front

What is the quadratic formula?

Back

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

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

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How do you factor a quadratic expression of the form x² + bx + c?

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To factor x² + bx + c, find two numbers that multiply to c and add to b, then rewrite the expression as (x + p)(x + q).

Front

What is the difference of squares?

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The difference of squares is a special factoring case where a² - b² = (a - b)(a + b).

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

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When a ≠ 1, use the method of grouping or the AC method: multiply a and c, find factors of that product that add to b, and rewrite the expression.

Front

What is the factored form of r² - 16r + 60?

Back

(r - 6)(r - 10)

Front

What is the factored form of x² + 9x - 36?

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(x + 12)(x - 3)