Factoring Quadratic Expressions

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, 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.

Front

What is the factored form of a quadratic expression?

Back

The factored form of a quadratic expression is expressed as (px + q)(rx + s), where p, q, r, and s are constants.

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).

Front

How do you factor x² - 16?

Back

x² - 16 can be factored as (x + 4)(x - 4) using the difference of squares.

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What is the first step in factoring a quadratic expression?

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The first step is to look for a common factor in all terms of the expression.

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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.

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How do you factor x² - 13x + 40?

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To factor x² - 13x + 40, find two numbers that multiply to 40 and add to -13. The factors are (x - 5)(x - 8).

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What is a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as a² + 2ab + b² = (a + b)².

Front

What is the factored form of x³ + 7x² - 2x - 14?

Back

The factored form is (x² - 2)(x + 7).