Factoring simple trinomials involves rewriting a trinomial (a polynomial with three terms) in its factored form, which is typically a product of two binomials. A trinomial generally has the form:

$ax^2 + bx + c$

For a simple trinomial, the coefficient $a = 1$, so the trinomial has the form:

$x^2 + bx + c$

Steps to Factor Simple Trinomials

1. Identify two numbers that:

   • Multiply to the constant term $c$.
   • Add to the middle coefficient $b$.

2. Rewrite the trinomial as a product of two binomials: $x^2 + bx + c = (x + p)(x + q)$ Where $p$ and $q$ are the two numbers found in Step 1.

Example

Factor $x^2 + 5x + 6$:

1. Look for two numbers that multiply to $6$ and add to $5$. These numbers are $2$ and $3$.
2. Rewrite as: $x^2 + 5x + 6 = (x + 2)(x + 3)$

The factors are $(x + 2)(x + 3)$.

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Another Example

Factor $x^2 - 7x + 10$:

1. Find two numbers that multiply to $10$ and add to $-7$: these are $-5$ and $-2$.
2. Rewrite as: $x^2 - 7x + 10 = (x - 5)(x - 2)$

The factors are $(x - 5)(x - 2)$.

Would you like additional examples or clarification?

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5 Related Questions

1. How do you factor trinomials when $a \neq 1$?
2. What if there are no two numbers that work for $b$ and $c$?
3. How can factoring be used to solve quadratic equations?
4. What are special cases, like perfect square trinomials?
5. How does factoring relate to the zero-product property?

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Tip

Always check your factors by multiplying them back together to ensure they produce the original trinomial!