Factoring Quadratics Mixed

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What is factoring in algebra?

Back

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?

Back

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 roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Front

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

Back

To factor x² + bx + c, find two numbers that multiply to c and add to b. These numbers will be used to write the expression as (x + p)(x + q), where p and q are the two numbers.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a² - b² = (a + b)(a - b).

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

Back

When a ≠ 1, use the method of grouping or the ac method. Multiply a and c, find two numbers that multiply to ac and add to b, then rewrite the expression and factor by grouping.

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What is the significance of the leading coefficient in a quadratic expression?

Back

The leading coefficient (a) affects the direction of the parabola's opening and its width. If a > 0, the parabola opens upwards; if a < 0, it opens downwards.

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.

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How do you factor a polynomial with a common factor?

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To factor a polynomial with a common factor, identify the greatest common factor (GCF) and factor it out of each term.

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What is the process of completing the square?

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Completing the square involves rewriting a quadratic in the form x² + bx + c into the form (x + p)² = q, making it easier to solve or graph.