We appreciate your visit to Factor tex 48x 3 12x 5 tex Write the answer as a product. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To factor the polynomial [tex]\(48 x^3 - 12 x^5\)[/tex], follow these steps:
1. Identify the Greatest Common Factor (GCF) of the coefficients.
- Look at the numbers 48 and 12.
- The GCF of 48 and 12 is 12.
2. Determine the lowest power of [tex]\(x\)[/tex] in the terms.
- We have [tex]\(x^3\)[/tex] and [tex]\(x^5\)[/tex].
- The lowest power of [tex]\(x\)[/tex] is [tex]\(x^3\)[/tex].
3. Factor out the GCF and the lowest power of [tex]\(x\)[/tex].
- From both terms, factor out 12 and [tex]\(x^3\)[/tex].
- This means we write [tex]\(48 x^3 - 12 x^5\)[/tex] as [tex]\(12 x^3 ( \frac{48}{12} \cdot x^{3-3} - \frac{12}{12} \cdot x^{5-3})\)[/tex].
4. Simplify inside the parentheses.
- [tex]\(48 \div 12 = 4\)[/tex], and [tex]\(x^{3-3} = x^0 = 1\)[/tex], so the first term becomes [tex]\(4\)[/tex].
- [tex]\(12 \div 12 = 1\)[/tex], and [tex]\(x^{5-3} = x^2\)[/tex], so the second term becomes [tex]\(x^2\)[/tex].
5. Write the final factored form.
- After factoring out [tex]\(12x^3\)[/tex], we get:
[tex]\[
12 x^3 (4 - x^2)
\][/tex]
So, the factored form of [tex]\(48 x^3 - 12 x^5\)[/tex] is:
[tex]\[
12 x^3 (4 - x^2)
\][/tex]
1. Identify the Greatest Common Factor (GCF) of the coefficients.
- Look at the numbers 48 and 12.
- The GCF of 48 and 12 is 12.
2. Determine the lowest power of [tex]\(x\)[/tex] in the terms.
- We have [tex]\(x^3\)[/tex] and [tex]\(x^5\)[/tex].
- The lowest power of [tex]\(x\)[/tex] is [tex]\(x^3\)[/tex].
3. Factor out the GCF and the lowest power of [tex]\(x\)[/tex].
- From both terms, factor out 12 and [tex]\(x^3\)[/tex].
- This means we write [tex]\(48 x^3 - 12 x^5\)[/tex] as [tex]\(12 x^3 ( \frac{48}{12} \cdot x^{3-3} - \frac{12}{12} \cdot x^{5-3})\)[/tex].
4. Simplify inside the parentheses.
- [tex]\(48 \div 12 = 4\)[/tex], and [tex]\(x^{3-3} = x^0 = 1\)[/tex], so the first term becomes [tex]\(4\)[/tex].
- [tex]\(12 \div 12 = 1\)[/tex], and [tex]\(x^{5-3} = x^2\)[/tex], so the second term becomes [tex]\(x^2\)[/tex].
5. Write the final factored form.
- After factoring out [tex]\(12x^3\)[/tex], we get:
[tex]\[
12 x^3 (4 - x^2)
\][/tex]
So, the factored form of [tex]\(48 x^3 - 12 x^5\)[/tex] is:
[tex]\[
12 x^3 (4 - x^2)
\][/tex]
Thanks for taking the time to read Factor tex 48x 3 12x 5 tex Write the answer as a product. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
