Factoring Polynomials

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 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 greatest common factor (GCF)?

Back

The GCF is the largest positive integer that divides each of the given integers without leaving a remainder.

Front

How do you find the GCF of two monomials?

Back

To find the GCF of two monomials, identify the common factors in their coefficients and the lowest power of each variable present in both monomials.

Front

Factor the polynomial: 2n^3 + 16n + 12

Back

2(n^3 + 8n + 6)

Front

Factor the polynomial: 56a^3 - 8a

Back

8a(7a^2 - 1)

Front

Factor the polynomial: 18a^2 - 15a

Back

3a(6a - 5)

Front

What is the first step in factoring a polynomial?

Back

The first step is to look for the greatest common factor (GCF) of all the terms in the polynomial.

Front

What does it mean to factor by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors from each group.

Front

What is a binomial?

Back

A binomial is a polynomial that consists of exactly two terms.