Factoring Trinomials and GCFs

Front

What is a trinomial?

Back

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

Front

What does GCF stand for in factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides all terms in a polynomial.

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, divide each term by the GCF, and express the polynomial as the product of the GCF and the resulting polynomial.

Front

Factor completely: 3x² + 18x + 15

Back

3(x + 5)(x + 1)

Front

What is the first step in factoring a trinomial?

Back

The first step is to check for a GCF and factor it out if it exists.

Front

Factor completely: 6x² + 5x - 6

Back

(3x - 2)(2x + 3)

Front

What is the purpose of factoring a polynomial?

Back

Factoring a polynomial simplifies it, making it easier to solve equations or analyze its properties.

Front

Factor completely: 5x² - 15x + 10

Back

5(x - 2)(x - 1)

Front

What is the difference between a prime polynomial and a factorable polynomial?

Back

A prime polynomial cannot be factored into simpler polynomials with integer coefficients, while a factorable polynomial can be expressed as a product of polynomials.

Front

Factor completely: 2m² + 3m - 9

Back

(m + 3)(2m - 3)