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Answer :
To factor the polynomial expression [tex]\(27x^6 + 36x^5 - 45x^3 + 18x\)[/tex], follow these steps:
1. Identify the Greatest Common Factor (GCF):
Begin by identifying the greatest common factor of all the terms in the expression. In this case, the GCF is [tex]\(9x\)[/tex], since each term is divisible by [tex]\(9x\)[/tex].
2. Factor out the GCF:
Once the GCF is identified, factor it out from the expression:
[tex]\[
27x^6 + 36x^5 - 45x^3 + 18x = 9x(3x^5 + 4x^4 - 5x^2 + 2)
\][/tex]
3. Check the Remaining Expression:
After factoring out the GCF, you should check if the remaining polynomial within the parentheses, [tex]\(3x^5 + 4x^4 - 5x^2 + 2\)[/tex], can be factored further. In this instance, the polynomial inside cannot be factored further using simple methods.
4. Final Factored Form:
The expression in its factored form is:
[tex]\[
9x(3x^5 + 4x^4 - 5x^2 + 2)
\][/tex]
This process provides you with a neatly factored polynomial, making it easier to work with or solve if it's part of an equation.
1. Identify the Greatest Common Factor (GCF):
Begin by identifying the greatest common factor of all the terms in the expression. In this case, the GCF is [tex]\(9x\)[/tex], since each term is divisible by [tex]\(9x\)[/tex].
2. Factor out the GCF:
Once the GCF is identified, factor it out from the expression:
[tex]\[
27x^6 + 36x^5 - 45x^3 + 18x = 9x(3x^5 + 4x^4 - 5x^2 + 2)
\][/tex]
3. Check the Remaining Expression:
After factoring out the GCF, you should check if the remaining polynomial within the parentheses, [tex]\(3x^5 + 4x^4 - 5x^2 + 2\)[/tex], can be factored further. In this instance, the polynomial inside cannot be factored further using simple methods.
4. Final Factored Form:
The expression in its factored form is:
[tex]\[
9x(3x^5 + 4x^4 - 5x^2 + 2)
\][/tex]
This process provides you with a neatly factored polynomial, making it easier to work with or solve if it's part of an equation.
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