Factoring Polynomials

Front

What is factoring in the context of polynomials?

Back

Factoring is the process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial.

Front

What is the standard form of a quadratic polynomial?

Back

The standard form of a quadratic polynomial is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials simplifies expressions, solves equations, and helps in graphing polynomial functions.

Front

What are the steps to factor a quadratic polynomial?

Back

1. Identify a, b, and c from the polynomial ax² + bx + c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the polynomial using these numbers. 4. Factor by grouping.

Front

What is the difference between factoring completely and factoring partially?

Back

Factoring completely means breaking down a polynomial into its irreducible factors, while factoring partially means factoring out common factors but not fully simplifying the expression.

Front

What is a common factor in polynomials?

Back

A common factor is a term that divides two or more terms in a polynomial without leaving a remainder.

Front

How do you factor a polynomial with a common factor?

Back

To factor a polynomial with a common factor, identify the greatest common factor (GCF) of the terms, factor it out, and rewrite the polynomial as the product of the GCF and the remaining polynomial.

Front

What is the difference of squares, and how is it factored?

Back

The difference of squares is a binomial of the form a² - b², which can be factored as (a - b)(a + b).

Front

What is the sum of cubes, and how is it factored?

Back

The sum of cubes is a binomial of the form a³ + b³, which can be factored as (a + b)(a² - ab + b²).

Front

What is the product of a sum and a difference?

Back

The product of a sum and a difference is expressed as (a + b)(a - b) = a² - b².