Flashcard 5 (Factoring and Solving Quadratics)

Front

What is the general form of a quadratic equation?

Back

The general 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 polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

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 solve a cubic equation like 5x³ - 7x² = 0?

Back

To solve a cubic equation like 5x³ - 7x² = 0, factor out the common term, which gives x²(5x - 7) = 0, leading to solutions x = 0 and x = 7/5.

Front

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.

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

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

How do you factor the expression 25x² - 9?

Back

The expression 25x² - 9 can be factored using the difference of squares formula: (5x + 3)(5x - 3).

Front

What is the process for solving a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, rewrite the equation in standard form, factor it into two binomials, set each factor equal to zero, and solve for x.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables raised to non-negative integer powers and coefficients.