Answer :

To factor the expression [tex]\(35x^2 + 25\)[/tex] completely, we begin by looking for the greatest common factor (GCF) of all the terms in the expression.

1. Find the GCF:

The expression has two terms: [tex]\(35x^2\)[/tex] and [tex]\(25\)[/tex].

- The GCF of the numerical coefficients 35 and 25 is 5 since both numbers are divisible by 5.
- Both terms do not share a common variable, so we only consider the numerical GCF.

2. Factor out the GCF:

We can factor the expression by taking the GCF, 5, out of each term:

- [tex]\(35x^2\)[/tex] divided by 5 is [tex]\(7x^2\)[/tex].
- [tex]\(25\)[/tex] divided by 5 is 5.

So, when we factor out the GCF, the expression becomes:

[tex]\[
5(7x^2 + 5)
\][/tex]

3. Check for further factoring:

Now, look inside the parentheses: [tex]\(7x^2 + 5\)[/tex]. This expression, [tex]\(7x^2 + 5\)[/tex], cannot be factored further because there are no common factors, and it does not fit any patterns like a difference of squares or a quadratic trinomial.

Thus, the complete factorization of the expression [tex]\(35x^2 + 25\)[/tex] is:

[tex]\[
5(7x^2 + 5)
\][/tex]

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