Flashcard 5 (Factoring and Solving Quadratics)

Front

What is factoring in algebra?

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 equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does it mean for a quadratic to be factored completely?

Back

A quadratic is factored completely when it is expressed as a product of linear factors, and no further factoring is possible.

Front

How do you factor the expression 3x² + 18x + 15?

Back

3(x + 5)(x + 1) is the complete factorization.

Front

What are the roots of the quadratic equation x² + 9x - 36?

Back

The roots are x = -12 and x = 3.

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 solve the quadratic equation 4x² - 16x - 9?

Back

The negative root is x = -1/2 or -0.5.

Front

What is the first step in factoring a polynomial like 5x³ - 7x²?

Back

The first step is to factor out the greatest common factor, which is x², giving x²(5x - 7).

Front

What are the factors of the quadratic 3x² - 17x + 10?

Back

The factors are (x - 5)(3x - 2).