Factoring by GCF, DOS or Guess & Check

Front

What is the GCF (Greatest Common Factor)?

Back

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

Front

How do you factor a polynomial using the GCF?

Back

1. Identify the GCF of the terms. 2. Divide each term by the GCF. 3. Write the polynomial as the product of the GCF and the resulting polynomial.

Front

What does DOS stand for in factoring?

Back

DOS stands for 'Difference of Squares', a method used to factor expressions of the form a² - b².

Front

What is the formula for factoring a difference of squares?

Back

The formula is a² - b² = (a + b)(a - b).

Front

What is the first step in the Guess & Check method for factoring?

Back

Identify the product and sum needed for the factors of the trinomial.

Front

If you have x² + 5x + 6, what two numbers multiply to 6 and add to 5?

Back

The numbers are 2 and 3.

Front

What is the result of factoring x² - 9?

Back

The result is (x + 3)(x - 3).

Front

What do you do to check your factoring work?

Back

Multiply the factors back together to see if you get the original polynomial.

Front

If a trinomial has a negative 'c' value, what can you conclude about its factors?

Back

One factor will be positive and the other will be negative.

Front

If a trinomial has a positive 'c' value, what can you conclude about its factors?

Back

Both factors will have the same sign, either both positive or both negative.