factoring questions
Understand the Problem
The question is referring to the topic of factoring in mathematics, which typically involves expressions or polynomials. The user is likely looking for help or examples of how to factor different types of mathematical expressions.
Answer
The expression factors to $(x + 2)(x + 3)$.
Answer for screen readers
The factored form of the expression $x^2 + 5x + 6$ is $(x + 2)(x + 3)$.
Steps to Solve
- Identify the expression to factor
First, determine the expression you need to factor. For example, let’s consider the expression $x^2 + 5x + 6$.
- Look for two numbers that multiply and add correctly
Find two numbers that multiply to give you the constant term (6, in this case) and add to give you the linear coefficient (5) from the expression. The numbers here are 2 and 3 because:
$$ 2 \times 3 = 6 $$ $$ 2 + 3 = 5 $$
- Write the expression as a product of factors
Using the numbers identified, write the factored form of the expression. This can be expressed as:
$$ (x + 2)(x + 3) $$
- Check your work
It’s always good to check the result by multiplying the factors back out to ensure they yield the original expression:
$$ (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6 $$
The result matches the original expression.
The factored form of the expression $x^2 + 5x + 6$ is $(x + 2)(x + 3)$.
More Information
Factoring is a key skill in algebra that helps simplify expressions and solve quadratic equations. Factoring can also provide insights into the roots of polynomials.
Tips
One common mistake is to overlook negative factors. For example, if the expression were $x^2 - 5x + 6$, some might mistakenly look for positive factors. Always ensure the signs of the factors reflect the signs in the original expression.
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