Answer :

To factor out the greatest common factor (GCF) from the expression [tex]\(35x^5 + 7x^3 + 7x^2\)[/tex], we can follow these steps:

1. Identify the GCF of the coefficients: Look at the numbers 35, 7, and 7. The GCF of these numbers is 7.

2. Identify the GCF of the variable parts: Consider the variable [tex]\(x\)[/tex] in each term:
- The first term is [tex]\(x^5\)[/tex], the second term is [tex]\(x^3\)[/tex], and the third term is [tex]\(x^2\)[/tex].
- The smallest power of [tex]\(x\)[/tex] across these terms is [tex]\(x^2\)[/tex].

3. Combine the GCFs: The GCF of the entire expression is the product of the GCFs of the coefficients and the variables, which is [tex]\(7x^2\)[/tex].

4. Factor out the GCF:
- Divide each term in the expression by the GCF, [tex]\(7x^2\)[/tex]:
- [tex]\(35x^5 \div 7x^2 = 5x^3\)[/tex]
- [tex]\(7x^3 \div 7x^2 = x\)[/tex]
- [tex]\(7x^2 \div 7x^2 = 1\)[/tex]

5. Write the factored expression: Putting it all together, the expression can be written as:
[tex]\[
7x^2(5x^3 + x + 1)
\][/tex]

So, the factored expression is [tex]\(7x^2(5x^3 + x + 1)\)[/tex].

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