Factoring & Solving by Factoring

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together give the original expression.

Front

What is the purpose of solving quadratic equations by factoring?

Back

The purpose is to find the values of the variable that make the equation true, often referred to as the roots or solutions of the equation.

Front

What is a quadratic equation?

Back

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

Front

What does it mean for a polynomial to be prime?

Back

A polynomial is considered prime if it cannot be factored into the product of two non-constant polynomials.

Front

What is the difference between a perfect square trinomial and a regular trinomial?

Back

A perfect square trinomial can be factored into the square of a binomial, while a regular trinomial cannot be expressed in this way.

Front

Factor the expression: x² - 4.

Back

(x - 2)(x + 2) - This is a difference of squares.

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

How do you factor the expression: x² + 5x + 6?

Back

(x + 2)(x + 3) - This is a trinomial that can be factored into two binomials.

Front

What is the first step in solving a quadratic equation by factoring?

Back

The first step is to set the equation to zero, typically by moving all terms to one side.

Front

What is the factored form of the expression: 2x² + 8x?

Back

2x(x + 4) - Factor out the greatest common factor.