# 8 Common Factorization Mistakes to Avoid

**Factoring polynomials** is an important algebra skill that involves breaking down a polynomial into its factors. While a useful technique, students often make mistakes when factoring which leads to incorrect solutions.

In this article, we will discuss how to avoid some common factorization mistakes.

**Common Factorization Mistakes**

These are some common factorization mistakes.

**1:Forgetting to Fully Factor**

Students may forget to factor a polynomial fully.

For example, factoring x^{2} + 5x + 6 as (x+3)(x+2). While (x+3) is a factor, the polynomial is not fully factored as there is still a common factor of (x+3) that can be taken out to get the fully factored form of (x+3)(x+2).

**2: Factoring the Wrong Common Factor**

When factoring trinomials of the form ax^{2} + bx + c, students may incorrectly factor out a number as the common factor rather than a variable.

For example, factoring 3x^{2} + 15x + 12 as 3(x^{2} + 5x + 4). The common factor is x, not 3. To avoid this, focus first on finding factors of the leading coefficient and constant that add or subtract to the middle term’s coefficient.

**3: Forgetting the Signs**

It’s easy to forget the proper signs when factoring polynomials.

For example, common mistake is writing -(x – 5)(x + 3) instead of -(x + 5)(x – 3). Be very careful about the signs of the factors when factoring the difference of two squares or polynomials with negative common factors.

**4: Making Sign Errors**

Another sign error that pops up is writing (x + 5)(x + 7) as the factored form of x^{2} – 12x + 35. The middle term is negative, not positive, so the factors should be (x + 5)(x – 7). Don’t rely on memorized formulas alone.

**5: Not Factoring Completely**

Some polynomials require multiple steps of factoring. Students may forget to factor in completely and stop early.

For example, only factoring x^{3} – 8 as x(x^{2} – 8) instead of the fully factored form x(x – 2)(x + 2). Always look for opportunities to factor further.

**6: Making Careless Mistakes**

Simple careless errors derail factorization. Accidentally leaving out a sign, swapping numbers, or losing a factor is easy to do when working quickly. Always double-check your factoring, verify the signs, and ensure no missing factors.

**7: Mixing Up Factorization Rules**

The numerous factorization rules and techniques are confusing for students. It’s easy to mix up the different methods or try to apply the wrong approach. Using flashcards or a study guide to review the factoring rules can help prevent errors.

**8: Relying on Calculators**

While calculators or math apps can factor polynomials, solely relying on these tools prevents building full factorization fluency.

Practice factoring manually to deepen understanding. Use technology to check your hand-factored forms and address any mistakes.

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