Factoring quadratics

Front

What is factoring in mathematics?

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.

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 is the standard form of a quadratic equation?

Back

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

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, found by setting the function equal to zero.

Front

How do you factor a perfect square trinomial?

Back

A perfect square trinomial can be factored as (a + b)² or (a - b)², where a² + 2ab + b² = (a + b)² and a² - 2ab + b² = (a - b)².

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 the expression x² - 16?

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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?

Back

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

Front

What does it mean if a quadratic expression is prime?

Back

A quadratic expression is prime if it cannot be factored into simpler linear factors with real coefficients.

Front

How do you factor the expression x² - 30x + 225?

Back

x² - 30x + 225 can be factored as (x - 15)², which is a perfect square trinomial.