When working with algebraic expressions, factoring is a common math operation. Factoring involves finding the factors of an algebraic expression, which are the terms that, when multiplied together, result in the original expression. In this article, we will explore the expression 10X^2 + 11X + 3 and determine which expression is a factor of it.
Understanding Factoring in Algebra
Before we dive into factoring the expression 10X^2 + 11X + 3, let’s review the basic principles of factoring in algebra. Factoring involves breaking down an algebraic expression into its simplest terms or factors. These factors can be numbers, variables, or a combination of both.
When factoring an expression, we are essentially looking for the terms that can be multiplied together to recreate the original expression. Understanding how to factor expressions is important in algebra as it plays a crucial role in solving equations, simplifying expressions, and finding solutions to various mathematical problems.
Factoring 10X^2 + 11X + 3
Now, let’s turn our attention to the expression 10X^2 + 11X + 3. To factor this expression, we need to find two binomials that, when multiplied together, give us the original expression.
One way to approach factoring is to look for two numbers that multiply to the product of the leading coefficient (10) and the constant term (3), which in this case is 30, and add up to the coefficient of the linear term (11).
- Factors of 30:
- 1 and 30
- 2 and 15
- 3 and 10
- 5 and 6
By examining the factors of 30, we can determine which pair adds up to 11. In this case, the pair 1 and 30, or 3 and 10 do not add up to 11, but the pair 2 and 15 does.
Now, we can rewrite the expression 10X^2 + 11X + 3 as follows:
10X^2 + 2X + 9X + 3
Next, we group the terms and factor by grouping:
2X(5X + 1) + 3(3)
Now, we can factor out the common factors to obtain the factored expression:
2X(5X + 1) + 3(3) = (2X + 3)(5X + 1)
Conclusion
In conclusion, by factoring the expression 10X^2 + 11X + 3, we have obtained the factors (2X + 3)(5X + 1). Factoring algebraic expressions is a useful skill in mathematics that allows us to simplify expressions, solve equations, and find solutions to various mathematical problems.
