Answer :

To factor the expression [tex]\(35x^2 + 63x^4\)[/tex] completely, follow these steps:

1. Identify the Greatest Common Factor (GCF):
First, look at the coefficients 35 and 63 and find their greatest common factor. The GCF of 35 and 63 is 7.
Next, look at the variable terms [tex]\(x^2\)[/tex] and [tex]\(x^4\)[/tex]. The smallest power is [tex]\(x^2\)[/tex]. Therefore, the GCF of the variable terms is [tex]\(x^2\)[/tex].

2. Factor out the GCF:
We will factor out [tex]\(7x^2\)[/tex] from the whole expression:

[tex]\[
35x^2 + 63x^4 = 7x^2(5 + 9x^2)
\][/tex]

3. Check for Further Factoring:
The expression inside the parentheses, [tex]\(5 + 9x^2\)[/tex], does not factor further using real numbers. So, our factorization is complete.

Thus, the completely factored form of the expression is:

[tex]\[
7x^2(9x^2 + 5)
\][/tex]

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Rewritten by : Barada