Answer :
To factor the expression [tex]\(21x^4 + 70x\)[/tex] completely, follow these steps:
1. Identify Common Factors: Look for any common factors in the terms of the expression. Both terms [tex]\(21x^4\)[/tex] and [tex]\(70x\)[/tex] have a common factor.
2. Extract the Greatest Common Factor (GCF): The greatest common factor of [tex]\(21x^4\)[/tex] and [tex]\(70x\)[/tex] is [tex]\(7x\)[/tex]. So, factor [tex]\(7x\)[/tex] out of the expression.
3. Factor the Expression:
[tex]\[
21x^4 + 70x = 7x(3x^3 + 10)
\][/tex]
When you factor out [tex]\(7x\)[/tex], you divide each term by [tex]\(7x\)[/tex]:
- [tex]\(21x^4 \div 7x = 3x^3\)[/tex]
- [tex]\(70x \div 7x = 10\)[/tex]
4. Write the Factored Expression: Therefore, the completely factored form of the expression is:
[tex]\[
7x(3x^3 + 10)
\][/tex]
That's the complete factorization of the given expression.
1. Identify Common Factors: Look for any common factors in the terms of the expression. Both terms [tex]\(21x^4\)[/tex] and [tex]\(70x\)[/tex] have a common factor.
2. Extract the Greatest Common Factor (GCF): The greatest common factor of [tex]\(21x^4\)[/tex] and [tex]\(70x\)[/tex] is [tex]\(7x\)[/tex]. So, factor [tex]\(7x\)[/tex] out of the expression.
3. Factor the Expression:
[tex]\[
21x^4 + 70x = 7x(3x^3 + 10)
\][/tex]
When you factor out [tex]\(7x\)[/tex], you divide each term by [tex]\(7x\)[/tex]:
- [tex]\(21x^4 \div 7x = 3x^3\)[/tex]
- [tex]\(70x \div 7x = 10\)[/tex]
4. Write the Factored Expression: Therefore, the completely factored form of the expression is:
[tex]\[
7x(3x^3 + 10)
\][/tex]
That's the complete factorization of the given expression.
