Answer :
To factor the expression [tex]\(21x^4 + 70x\)[/tex] completely, we can follow these steps:
1. Look for a common factor in all terms.
Both terms in the expression, [tex]\(21x^4\)[/tex] and [tex]\(70x\)[/tex], have a common factor. Let's identify it:
- The coefficients 21 and 70 have a greatest common factor (GCF) of 7.
- Also, the variable [tex]\(x\)[/tex] is present in both terms. We can factor out the lowest power, which is [tex]\(x^1\)[/tex].
So, the common factor in the expression is [tex]\(7x\)[/tex].
2. Factor out the common term.
We can factor out [tex]\(7x\)[/tex] from each term in the expression:
[tex]\[
21x^4 + 70x = 7x(3x^3 + 10)
\][/tex]
3. Check if the expression inside the parentheses can be factored further.
Now, look at the expression inside the parentheses: [tex]\(3x^3 + 10\)[/tex].
- There aren't any common factors other than 1.
- The polynomial [tex]\(3x^3 + 10\)[/tex] cannot be factored further using simple means as it is not a standard factorable form like a difference of squares or a perfect cube.
Since [tex]\(3x^3 + 10\)[/tex] is already simplified, the completely factored form of the expression [tex]\(21x^4 + 70x\)[/tex] is:
[tex]\[
7x(3x^3 + 10)
\][/tex]
This is the complete factorization of the original expression.
1. Look for a common factor in all terms.
Both terms in the expression, [tex]\(21x^4\)[/tex] and [tex]\(70x\)[/tex], have a common factor. Let's identify it:
- The coefficients 21 and 70 have a greatest common factor (GCF) of 7.
- Also, the variable [tex]\(x\)[/tex] is present in both terms. We can factor out the lowest power, which is [tex]\(x^1\)[/tex].
So, the common factor in the expression is [tex]\(7x\)[/tex].
2. Factor out the common term.
We can factor out [tex]\(7x\)[/tex] from each term in the expression:
[tex]\[
21x^4 + 70x = 7x(3x^3 + 10)
\][/tex]
3. Check if the expression inside the parentheses can be factored further.
Now, look at the expression inside the parentheses: [tex]\(3x^3 + 10\)[/tex].
- There aren't any common factors other than 1.
- The polynomial [tex]\(3x^3 + 10\)[/tex] cannot be factored further using simple means as it is not a standard factorable form like a difference of squares or a perfect cube.
Since [tex]\(3x^3 + 10\)[/tex] is already simplified, the completely factored form of the expression [tex]\(21x^4 + 70x\)[/tex] is:
[tex]\[
7x(3x^3 + 10)
\][/tex]
This is the complete factorization of the original expression.
