Drag the Tiles to the Correct Boxes

Oct 13, 2025 by talynt.org 102 views

Introduction

Factoring an expression is a crucial step in solving algebraic equations and inequalities. One of the methods used to factor an expression is the grouping method. This method involves rearranging the terms of the expression into groups that can be factored using the difference of squares or the sum and difference of two terms. In this article, we will arrange the steps from start to finish to factor the expression $x^2 - 5x - 24$ using the grouping method.

Step 1: Write Down the Expression

The given expression is $x^2 - 5x - 24$ . We will start by writing down the expression.

x^2 - 5x - 24

Step 2: Rearrange the Terms

To factor the expression using the grouping method, we need to rearrange the terms into two groups. We can do this by grouping the first two terms together and the last two terms together.

(x^2 - 5x) + (-24)

Step 3: Factor the First Group

The first group is $(x^2 - 5x)$ . We can factor out the common term $x$ from this group.

x(x - 5)

Step 4: Factor the Second Group

The second group is $(-24)$ . We can factor out the common term $-1$ from this group.

-1(-24)

Step 5: Rewrite the Expression

Now that we have factored the first and second groups, we can rewrite the expression as follows:

x(x - 5) - 1(-24)

Step 6: Factor the Expression

We can now factor the expression using the difference of squares formula.

(x - 3)(x + 8)

Conclusion

In this article, we have arranged the steps from start to finish to factor the expression $x^2 - 5x - 24$ using the grouping method. We started by writing down the expression, rearranging the terms, factoring the first group, factoring the second group, rewriting the expression, and finally factoring the expression using the difference of squares formula.

Discussion

The grouping method is a useful technique for factoring expressions. It involves rearranging the terms of the expression into groups that can be factored using the difference of squares or the sum and difference of two terms. This method can be used to factor a wide range of expressions, including quadratic expressions, polynomial expressions, and rational expressions.

Tiles

The following tiles can be used to factor the expression $x^2 - 5x - 24$ using the grouping method:

$(x-3)(x+8)$
$\left(x^2+3x\right)+(-8x-24)$

Drag the Tiles to the Correct Boxes

Not all tiles will be used. Drag the tiles to the correct boxes to factor the expression $x^2 - 5x - 24$ using the grouping method.

Answer

The correct answer is:

$(x-3)(x+8)$
$\left(x^2+3x\right)+(-8x-24)$

Explanation

The expression $x^2 - 5x - 24$ can be factored using the grouping method as follows:

Write down the expression: $x^2 - 5x - 24$
Rearrange the terms: $(x^2 - 5x) + (-24)$
Factor the first group: $x(x - 5)$
Factor the second group: $-1(-24)$
Rewrite the expression: $x(x - 5) - 1(-24)$
Factor the expression: $(x - 3)(x + 8)$

Q: What is the grouping method for factoring expressions?

A: The grouping method is a technique used to factor expressions by rearranging the terms into groups that can be factored using the difference of squares or the sum and difference of two terms.

Q: How do I start factoring an expression using the grouping method?

A: To start factoring an expression using the grouping method, you need to write down the expression and rearrange the terms into two groups.

Q: What are the steps to factor the expression $x^2 - 5x - 24$ using the grouping method?

A: The steps to factor the expression $x^2 - 5x - 24$ using the grouping method are as follows:

Write down the expression: $x^2 - 5x - 24$
Rearrange the terms: $(x^2 - 5x) + (-24)$
Factor the first group: $x(x - 5)$
Factor the second group: $-1(-24)$
Rewrite the expression: $x(x - 5) - 1(-24)$
Factor the expression: $(x - 3)(x + 8)$

Q: What is the difference of squares formula?

A: The difference of squares formula is $(a - b)(a + b) = a^2 - b^2$ .

Q: How do I use the difference of squares formula to factor an expression?

A: To use the difference of squares formula to factor an expression, you need to identify two terms that are squares and can be written in the form $(a - b)$ and $(a + b)$ .

Q: What are some common mistakes to avoid when factoring expressions using the grouping method?

A: Some common mistakes to avoid when factoring expressions using the grouping method are:

Not rearranging the terms into groups
Not factoring the first group
Not factoring the second group
Not rewriting the expression
Not factoring the expression using the difference of squares formula

Q: How do I check if my factored expression is correct?

A: To check if your factored expression is correct, you need to multiply the factors together and simplify the expression.

Q: What are some real-world applications of factoring expressions using the grouping method?

A: Some real-world applications of factoring expressions using the grouping method are:

Solving quadratic equations
Finding the roots of a polynomial equation
Factoring rational expressions
Solving systems of linear equations

Q: Can I use the grouping method to factor any type of expression?

A: Yes, you can use the grouping method to factor any type of expression, including quadratic expressions, polynomial expressions, and rational expressions.

Q: What are some tips for factoring expressions using the grouping method?

A: Some tips for factoring expressions using the grouping method are:

Make sure to rearrange the terms into groups
Factor the first group
Factor the second group
Rewrite the expression
Factor the expression using the difference of squares formula

Conclusion

In this article, we have answered some common questions about factoring the expression $x^2 - 5x - 24$ using the grouping method. We have covered the steps to factor the expression, the difference of squares formula, common mistakes to avoid, and real-world applications of factoring expressions using the grouping method. We have also provided some tips for factoring expressions using the grouping method.