Factoring Polynomials GCF

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest positive integer that divides all the coefficients of a polynomial without leaving a remainder.

Front

How do you find the GCF of two numbers, for example, 10 and 15?

Back

To find the GCF of 10 and 15, list the factors of each number: Factors of 10 are 1, 2, 5, 10; Factors of 15 are 1, 3, 5, 15. The GCF is 5.

Front

What is the first step in factoring a polynomial like 10x + 15?

Back

The first step is to identify the GCF of the coefficients (10 and 15), which is 5.

Front

How do you factor the expression 10x + 15 using the GCF?

Back

Factor out the GCF (5) from the expression: 10x + 15 = 5(2x + 3).

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means rewriting it as a product of its factors, which can be numbers, variables, or both.

Front

Can you factor the expression 3x^2 + 6x? If so, how?

Back

Yes, factor out the GCF, which is 3x: 3x^2 + 6x = 3x(x + 2).

Front

What is the significance of factoring in algebra?

Back

Factoring is significant because it simplifies expressions, makes solving equations easier, and helps in graphing polynomials.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

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

How do you check if your factoring is correct?

Back

You can check your factoring by multiplying the factors back together to see if you obtain the original expression.