Factoring Quadratics

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the general method for factoring quadratics?

Back

The general method for factoring quadratics involves finding two numbers that multiply to 'ac' (the product of a and c) and add to 'b' (the coefficient of x).

Front

What are the factors of the quadratic expression x² + 2x - 24?

Back

The factors are (x + 6)(x - 4).

Front

How do you determine the roots of a quadratic equation?

Back

The roots of a quadratic equation can be determined by factoring, completing the square, or using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What are the factors of the quadratic expression x² + 25x + 24?

Back

The factors are (x + 24)(x + 1).

Front

What is the relationship between the coefficients of a quadratic and its roots?

Back

The sum of the roots is equal to -b/a and the product of the roots is equal to c/a.

Front

What are the factors of the quadratic expression x² + 5x - 24?

Back

The factors are (x + 8)(x - 3).

Front

How can you check if your factorization of a quadratic is correct?

Back

You can check by multiplying the factors back together to see if you obtain the original quadratic expression.