How do you factor binomials?
Understand the Problem
The question is asking for the process or method used to factor binomials in algebra. This involves identifying common factors or applying formulas to simplify the expression.
Answer
Identify the GCF, rewrite, factor out the GCF, and apply special formulas if applicable.
Answer for screen readers
You factor binomials by identifying the greatest common factor, rewriting the binomial using the GCF, factoring out the GCF, and applying special binomial formulas if applicable.
Steps to Solve
- Identify the greatest common factor (GCF)
Identify the largest factor that divides both terms in the binomial.
Example: For the binomial $6x^2 - 9x$, the GCF is $3x$.
- Rewrite the binomial using the GCF
Express each term as a product of the GCF and another term.
$$6x^2 - 9x = 3x(2x) - 3x(3)$$
- Factor out the GCF
Remove the GCF from each term, and write it outside the parentheses.
$$6x^2 - 9x = 3x(2x - 3)$$
- Use special binomial formulas if applicable
For some binomials, special factorization formulas might apply, such as the difference of squares or perfect square trinomials.
- Difference of squares: $a^2 - b^2 = (a - b)(a + b)$
- Perfect square trinomials: $(a - b)^2 = a^2 - 2ab + b^2$
- Apply the relevant formula to factorize
Check if the binomial fits any of the special formulas, and apply the relevant factorizations.
Example: For $x^2 - 9$, apply the difference of squares formula:
$$x^2 - 9 = x^2 - 3^2 = (x - 3)(x + 3)$$
You factor binomials by identifying the greatest common factor, rewriting the binomial using the GCF, factoring out the GCF, and applying special binomial formulas if applicable.
More Information
Factoring binomials is a fundamental skill in algebra that simplifies expressions and solves equations.
Tips
A common mistake is forgetting to factor out the GCF completely, or misapplying special formulas. Always double-check each term after factoring.