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 that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the difference between a monomial, binomial, and trinomial?

Back

A monomial has one term, a binomial has two terms, and a trinomial has three terms.

Front

What is the purpose of factoring polynomials?

Back

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

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that divides two or more numbers or terms without leaving a remainder.

Front

How do you factor a quadratic polynomial in the form ax^2 + bx + c?

Back

To factor a quadratic polynomial, find two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the middle term using these numbers and factor by grouping.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a^2 - b^2 = (a - b)(a + b).

Front

What is a perfect square trinomial?

Back

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

Front

How do you factor the expression x^2 - 36?

Back

x^2 - 36 can be factored as (x + 6)(x - 6) using the difference of squares.

Front

What is the factored form of 3v^2 - 4v - 7?

Back

The factored form is (3v - 7)(v + 1).