Factoring Polynomials

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 polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does GCF stand for in factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers or expressions.

Front

How do you factor by grouping?

Back

To factor by grouping, you group terms with common factors, factor out the GCF from each group, and then factor out the common binomial factor.

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax^2 + bx + c.

Front

What is the first step in factoring a polynomial?

Back

The first step is to look for the GCF of all the terms in the polynomial and factor it out.

Front

How do you factor the trinomial 9x^2 - 6x - 8?

Back

The trinomial can be factored as (3x + 2)(3x - 4).

Front

What is the result of factoring 5n³ - 10n² + 3n - 6?

Back

The expression factors to (5n² + 3)(n - 2).

Front

What is the factored form of 3x³ + 9x² - 15x?

Back

The expression factors to 3x(x² + 3x - 5).

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials simplifies expressions, makes solving equations easier, and helps in graphing polynomial functions.