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Answer :
Let's factor the expression [tex]\( 21x^4 + 70x \)[/tex] completely, step-by-step.
1. Identify the Greatest Common Factor (GCF):
- Look at the coefficients 21 and 70. The GCF of these numbers is 7.
- Look at the variable part. The smallest power of [tex]\( x \)[/tex] in both terms is [tex]\( x^1 \)[/tex].
- Therefore, the GCF of the expression is [tex]\( 7x \)[/tex].
2. Factor out the GCF:
- Divide each term by the GCF [tex]\( 7x \)[/tex].
- For the first term: [tex]\( \frac{21x^4}{7x} = 3x^3 \)[/tex].
- For the second term: [tex]\( \frac{70x}{7x} = 10 \)[/tex].
3. Write the factored expression:
- The expression [tex]\( 21x^4 + 70x \)[/tex] can be factored as:
[tex]\[
21x^4 + 70x = 7x(3x^3 + 10)
\][/tex]
Therefore, the completely factored expression is [tex]\( 7x(3x^3 + 10) \)[/tex].
1. Identify the Greatest Common Factor (GCF):
- Look at the coefficients 21 and 70. The GCF of these numbers is 7.
- Look at the variable part. The smallest power of [tex]\( x \)[/tex] in both terms is [tex]\( x^1 \)[/tex].
- Therefore, the GCF of the expression is [tex]\( 7x \)[/tex].
2. Factor out the GCF:
- Divide each term by the GCF [tex]\( 7x \)[/tex].
- For the first term: [tex]\( \frac{21x^4}{7x} = 3x^3 \)[/tex].
- For the second term: [tex]\( \frac{70x}{7x} = 10 \)[/tex].
3. Write the factored expression:
- The expression [tex]\( 21x^4 + 70x \)[/tex] can be factored as:
[tex]\[
21x^4 + 70x = 7x(3x^3 + 10)
\][/tex]
Therefore, the completely factored expression is [tex]\( 7x(3x^3 + 10) \)[/tex].
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