Factoring and Solve by Factoring, a=1

Front

What is factoring in mathematics?

Back

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

Front

What does it mean to solve by factoring?

Back

To solve by factoring means to set an equation to zero and factor the polynomial, then use the zero product property to find the values of the variable.

Front

What are the roots of a polynomial?

Back

The roots of a polynomial are the values of the variable that make the polynomial equal to zero.

Front

Define the term 'zeros' in relation to polynomials.

Back

Zeros are the values of the variable that make the polynomial equal to zero; they are synonymous with roots.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

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 a quadratic equation in the form ax^2 + bx + c?

Back

To factor a quadratic equation, look for two numbers that multiply to ac (the product of a and c) and add to b. Rewrite the equation using these numbers to factor it.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (a + b)^2 = a^2 + 2ab + b^2.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the difference between factoring and expanding?

Back

Factoring is breaking down an expression into simpler components, while expanding is multiplying out the components to form a single expression.