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 are the factors of the expression 4x² - 49?

Back

(2x - 7)(2x + 7)

Front

What is the GCF (Greatest Common Factor) of the expression 8n⁴ - 4n² + 36n?

Back

4n

Front

What is the other factor of the expression x² - x - 20 if one factor is (x - 5)?

Back

(x + 4)

Front

What does it mean for an expression to be prime?

Back

An expression is prime if it cannot be factored into simpler expressions with integer coefficients.

Front

How do you factor a quadratic expression in the form ax² + bx + c?

Back

To factor a quadratic expression, find two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the expression using these numbers.

Front

What is the difference between factoring and expanding an expression?

Back

Factoring is breaking down an expression into products, while expanding is multiplying out the factors to get the original expression.

Front

What is the factored form of the expression 2x² + 4x + 3?

Back

none of these (it cannot be factored over the integers).

Front

What is the significance of the quadratic formula?

Back

The quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), provides the solutions to a quadratic equation ax² + bx + c = 0.