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Answer :
To factor the expression [tex]\(30x - 70x^4\)[/tex] completely, follow these steps:
1. Identify the Greatest Common Factor (GCF):
First, find the GCF of the coefficients and the lowest power of [tex]\(x\)[/tex]. The coefficients are 30 and 70. The greatest common factor of these numbers is 10. For the variable part, [tex]\(x\)[/tex] is present in both terms, and the smallest power is [tex]\(x^1\)[/tex].
2. Factor out the GCF:
Pull out the GCF from the expression:
[tex]\[
30x - 70x^4 = 10x(3 - 7x^3)
\][/tex]
3. Check for Further Factoring:
Look at the expression inside the parentheses: [tex]\(3 - 7x^3\)[/tex]. Check if it can be factored further. In this case, [tex]\(3 - 7x^3\)[/tex] doesn't factor further using integers or simple algebraic identities.
4. Write the Fully Factored Expression:
The completely factored form of the expression is:
[tex]\[
-10x(7x^3 - 3)
\][/tex]
This is the final factored expression for [tex]\(30x - 70x^4\)[/tex].
1. Identify the Greatest Common Factor (GCF):
First, find the GCF of the coefficients and the lowest power of [tex]\(x\)[/tex]. The coefficients are 30 and 70. The greatest common factor of these numbers is 10. For the variable part, [tex]\(x\)[/tex] is present in both terms, and the smallest power is [tex]\(x^1\)[/tex].
2. Factor out the GCF:
Pull out the GCF from the expression:
[tex]\[
30x - 70x^4 = 10x(3 - 7x^3)
\][/tex]
3. Check for Further Factoring:
Look at the expression inside the parentheses: [tex]\(3 - 7x^3\)[/tex]. Check if it can be factored further. In this case, [tex]\(3 - 7x^3\)[/tex] doesn't factor further using integers or simple algebraic identities.
4. Write the Fully Factored Expression:
The completely factored form of the expression is:
[tex]\[
-10x(7x^3 - 3)
\][/tex]
This is the final factored expression for [tex]\(30x - 70x^4\)[/tex].
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