Question

How can you factor binomials and trinomials in one variable?

Answer 1

To factor binomials and trinomials in one variable, you look for the common factors in the terms

How to factor a binomial and trinomial?

Binomials are polynomials with two terms while trinomial have three terms.

For instance, we have:

• Binomial: x^2 - 4
• Trinomial = x^2 + 4x + 4

To factor x^2 - 4, we use the following steps:

x^2 - 4

Express 4 as 2^2

x^2 - 4 = x^2 - 2^2

Apply the difference of two squares

x^2 - 4 = (x - 2)(x + 2)

To factor x^2 + 4x + 4 we use the following steps:

x^2 + 4x + 4

Express 4x as 2x + 2x

x^2 + 4x + 4 = x^2 + 2x + 2x + 4

Factorize

x^2 + 4x + 4 = x(x + 2) + 2(x + 2)

Factor out x + 2

x^2 + 4x + 4 = (x + 2)x + 2)

Rewrite as:

x^2 + 4x + 4 = (x + 2)^2

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Answer 2

To factor binomials and trinomials in one variable, you look for the common factors in the terms below.

What is Polynomial?

A polynomial is a type of expression. An expression is a mathematical statement without an equal-to sign (=).

Binomial: x² - 4

Trinomial = x² + 4x + 4

To factor x² - 4, we use the following steps:

x² - 4 = x² - 2²

x² - 4 = (x - 2)(x + 2)

To factor x² + 4x + 4 we use the following steps:

x² + 4x + 4

x² + 4x + 4 = x² + 2x + 2x + 4

x² + 4x + 4 = x(x + 2) + 2(x + 2)

Factor out x + 2

x² + 4x + 4 = (x + 2)²

Learn more about polynomials at:

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