Factoring Quadratic Expressions a>1

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 involves rewriting it as a product of two binomials.

Front

What is the standard form of a quadratic expression?

Back

The standard form of a quadratic expression is ax² + bx + c.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a + b)(a - b).

Front

How do you factor x² - 144?

Back

x² - 144 can be factored using the difference of squares formula: (x + 12)(x - 12).

Front

What is the first step in factoring a quadratic expression?

Back

The first step is to look for a common factor in all terms, if one exists.

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

How do you factor 6x² - 19x - 7?

Back

To factor 6x² - 19x - 7, find two numbers that multiply to (6 * -7) = -42 and add to -19. The factors are (2x - 7)(3x + 1).

Front

What is a binomial?

Back

A binomial is a polynomial with two terms, such as (x + 3) or (2x - 5).

Front

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

Back

The leading coefficient (a) determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.