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Answer :
To solve the expression [tex]\(48x - 48x^3 - 18x^4\)[/tex], we can follow these steps:
1. Identify the Expression:
Begin with the given polynomial expression:
[tex]\[
48x - 48x^3 - 18x^4
\][/tex]
2. Arrange the Terms:
Arrange the terms of the polynomial in descending order with respect to the powers of [tex]\(x\)[/tex]:
[tex]\[
-18x^4 - 48x^3 + 48x
\][/tex]
3. Factor Out the Common Term:
Check if there is a common factor in all the terms. Here, each term contains a factor of [tex]\(x\)[/tex]. The greatest common factor (GCF) among the coefficients is 6. Therefore, we can factor out [tex]\(6x\)[/tex]:
[tex]\[
= 6x(-3x^3 - 8x^2 + 8)
\][/tex]
4. Conclusion:
The simplified expression is:
[tex]\[
-18x^4 - 48x^3 + 48x
\][/tex]
This matches with the terms arranged in step 2. Hence, the expression in the simplest arranged form is ready for further analysis or use in other calculations.
These steps provide a clear understanding of how to manipulate and simplify the polynomial, presenting it in an organized way.
1. Identify the Expression:
Begin with the given polynomial expression:
[tex]\[
48x - 48x^3 - 18x^4
\][/tex]
2. Arrange the Terms:
Arrange the terms of the polynomial in descending order with respect to the powers of [tex]\(x\)[/tex]:
[tex]\[
-18x^4 - 48x^3 + 48x
\][/tex]
3. Factor Out the Common Term:
Check if there is a common factor in all the terms. Here, each term contains a factor of [tex]\(x\)[/tex]. The greatest common factor (GCF) among the coefficients is 6. Therefore, we can factor out [tex]\(6x\)[/tex]:
[tex]\[
= 6x(-3x^3 - 8x^2 + 8)
\][/tex]
4. Conclusion:
The simplified expression is:
[tex]\[
-18x^4 - 48x^3 + 48x
\][/tex]
This matches with the terms arranged in step 2. Hence, the expression in the simplest arranged form is ready for further analysis or use in other calculations.
These steps provide a clear understanding of how to manipulate and simplify the polynomial, presenting it in an organized way.
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