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Answer :
Certainly! Let's take a closer look at the polynomial expression [tex]\(53x^5 - 35x^3\)[/tex].
1. Understanding the Expression:
- This expression is a polynomial of degree 5, since the highest power of [tex]\(x\)[/tex] is 5.
- The expression is [tex]\(53x^5 - 35x^3\)[/tex], consisting of two terms:
- [tex]\(53x^5\)[/tex] and
- [tex]\(-35x^3\)[/tex].
2. Factoring Out Common Terms:
- First, we look for a common factor in both terms. Both terms have a factor of [tex]\(x^3\)[/tex].
- Therefore, we can factor [tex]\(x^3\)[/tex] out of the expression.
3. Factoring Process:
- By factoring out [tex]\(x^3\)[/tex], we rewrite the expression as:
[tex]\[
x^3(53x^2 - 35)
\][/tex]
- Here, [tex]\(x^3\)[/tex] is the common factor that we've factored out.
4. Simplified Form:
- The factored form [tex]\(x^3(53x^2 - 35)\)[/tex] is the simplest way to express the polynomial.
5. Conclusion:
- This expression is now simplified and does not have any further common factors. Thus, the expression [tex]\(53x^5 - 35x^3\)[/tex] is expressed in its simplest factorized form as [tex]\(x^3(53x^2 - 35)\)[/tex].
This is the detailed breakdown of the polynomial, showing that it is simplified by factoring out the common factor.
1. Understanding the Expression:
- This expression is a polynomial of degree 5, since the highest power of [tex]\(x\)[/tex] is 5.
- The expression is [tex]\(53x^5 - 35x^3\)[/tex], consisting of two terms:
- [tex]\(53x^5\)[/tex] and
- [tex]\(-35x^3\)[/tex].
2. Factoring Out Common Terms:
- First, we look for a common factor in both terms. Both terms have a factor of [tex]\(x^3\)[/tex].
- Therefore, we can factor [tex]\(x^3\)[/tex] out of the expression.
3. Factoring Process:
- By factoring out [tex]\(x^3\)[/tex], we rewrite the expression as:
[tex]\[
x^3(53x^2 - 35)
\][/tex]
- Here, [tex]\(x^3\)[/tex] is the common factor that we've factored out.
4. Simplified Form:
- The factored form [tex]\(x^3(53x^2 - 35)\)[/tex] is the simplest way to express the polynomial.
5. Conclusion:
- This expression is now simplified and does not have any further common factors. Thus, the expression [tex]\(53x^5 - 35x^3\)[/tex] is expressed in its simplest factorized form as [tex]\(x^3(53x^2 - 35)\)[/tex].
This is the detailed breakdown of the polynomial, showing that it is simplified by factoring out the common factor.
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