Factoring Review (GCF, DOS, Basic Trinomials)

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 factor out the GCF from a polynomial?

Back

To factor out the GCF, identify the largest factor common to all terms, then divide each term by the GCF and write it outside the parentheses.

Front

Factor the expression completely: 3x² + 18x + 15

Back

3(x + 5)(x + 1)

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax² + bx + c.

Front

How do you factor a basic trinomial?

Back

To factor a basic trinomial, find two numbers that multiply to 'c' and add to 'b', then express the trinomial as a product of two binomials.

Front

Factor the expression: 4x² - 20x + 25

Back

(2x - 5)(2x - 5)

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern where a² - b² = (a + b)(a - b).

Front

Factor the expression: 56a³ - 8a

Back

8a(7a² - 1)

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a trinomial that can be expressed as the square of a binomial, such as (a + b)² = a² + 2ab + b².

Front

Factor the expression: 10x² + 15x - 5

Back

5(2x² + 3x - 1)