At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Sure, let's go through the process of factoring the expression step-by-step to identify the correct answer.
Given expression:
[tex]\[ 5x^2 - 45 \][/tex]
### Step 1: Factor out the Greatest Common Factor (GCF)
First, we identify the greatest common factor of the terms in the expression. Here, 5 is the GCF of the terms [tex]\(5x^2\)[/tex] and [tex]\(-45\)[/tex]:
[tex]\[ 5x^2 - 45 = 5(x^2 - 9) \][/tex]
### Step 2: Recognize and apply the difference of squares
Next, we notice that [tex]\(x^2 - 9\)[/tex] is a difference of squares. Recall that a difference of squares can be factored using the formula:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In this case, [tex]\(x^2 - 9\)[/tex] fits the structure of a difference of squares, where:
[tex]\[ x^2 - 9 = x^2 - 3^2 \][/tex]
Applying the difference of squares formula:
[tex]\[ x^2 - 3^2 = (x - 3)(x + 3) \][/tex]
Therefore, we further factor [tex]\(5(x^2 - 9)\)[/tex] as follows:
[tex]\[ 5(x^2 - 9) = 5(x - 3)(x + 3) \][/tex]
### Conclusion
The completely factored form of [tex]\(5x^2 - 45\)[/tex] is:
[tex]\[ 5(x - 3)(x + 3) \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
Thus, the option C, [tex]\(5(x + 3)(x - 3)\)[/tex], is the correct factorization of the given expression.
Given expression:
[tex]\[ 5x^2 - 45 \][/tex]
### Step 1: Factor out the Greatest Common Factor (GCF)
First, we identify the greatest common factor of the terms in the expression. Here, 5 is the GCF of the terms [tex]\(5x^2\)[/tex] and [tex]\(-45\)[/tex]:
[tex]\[ 5x^2 - 45 = 5(x^2 - 9) \][/tex]
### Step 2: Recognize and apply the difference of squares
Next, we notice that [tex]\(x^2 - 9\)[/tex] is a difference of squares. Recall that a difference of squares can be factored using the formula:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In this case, [tex]\(x^2 - 9\)[/tex] fits the structure of a difference of squares, where:
[tex]\[ x^2 - 9 = x^2 - 3^2 \][/tex]
Applying the difference of squares formula:
[tex]\[ x^2 - 3^2 = (x - 3)(x + 3) \][/tex]
Therefore, we further factor [tex]\(5(x^2 - 9)\)[/tex] as follows:
[tex]\[ 5(x^2 - 9) = 5(x - 3)(x + 3) \][/tex]
### Conclusion
The completely factored form of [tex]\(5x^2 - 45\)[/tex] is:
[tex]\[ 5(x - 3)(x + 3) \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
Thus, the option C, [tex]\(5(x + 3)(x - 3)\)[/tex], is the correct factorization of the given expression.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.