Factoring Quadratic Expressions

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 means rewriting it as a product of its linear factors, typically in the form (px + q)(rx + s).

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 factored form of (x-1)(x-9)?

Back

x² - 10x + 9.

Front

How do you factor the expression 5n² - 6n - 27?

Back

(5n - 9)(n + 3).

Front

What is the factored form of 4x² - 20x + 25?

Back

(2x - 5)².

Front

How do you factor the expression 6x² + 7x - 3?

Back

(2x + 3)(3x - 1).

Front

What is the sum of (3x² - 12) + (9x² + 4x - 1)?

Back

12x² + 4x - 13.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.