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 does GCF stand for in factoring?

Back

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

Front

What is the first step in factoring a polynomial?

Back

The first step is often to look for the GCF of the terms in the polynomial.

Front

How do you factor the polynomial x^2 + x - 6?

Back

The factors are (x + 3)(x - 2).

Front

What are the factors of 5n^2 + 11n - 12?

Back

The factors are (5n - 4)(n + 3).

Front

How do you find the factors of a quadratic polynomial?

Back

To find the factors of a quadratic polynomial, look for two numbers that multiply to the constant term and add to the coefficient of the linear term.

Front

What is the factored form of 2b^2 + 14b - 16?

Back

The factored form is 2(b - 1)(b + 8).

Front

What is the significance of the constant term in factoring?

Back

The constant term helps identify the pairs of factors that can be used to break down the polynomial.

Front

What is the process of listing factors?

Back

Listing factors involves identifying all pairs of numbers that multiply to give a specific product, such as the constant term in a polynomial.