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Answer :
To factor the expression [tex]\(35x^2 + 25\)[/tex] completely, follow these steps:
1. Identify Common Factors: Look for the greatest common factor (GCF) of the terms in the expression. The expression has two terms: [tex]\(35x^2\)[/tex] and [tex]\(25\)[/tex].
2. Find the GCF: The coefficients of the terms are 35 and 25. The greatest common factor of 35 and 25 is 5.
3. Factor Out the GCF: Divide both terms of the expression by the GCF (5) and express the original expression as a product:
[tex]\[
35x^2 + 25 = 5(7x^2 + 5)
\][/tex]
4. Check for Further Factorization: After factoring out the GCF, check if the remaining expression inside the parentheses, [tex]\(7x^2 + 5\)[/tex], can be factored further. Since [tex]\(7x^2 + 5\)[/tex] is a sum of terms with no common factors and neither term can be factored further, this is the simplest form.
The completely factored form of the expression [tex]\(35x^2 + 25\)[/tex] is [tex]\(5(7x^2 + 5)\)[/tex].
1. Identify Common Factors: Look for the greatest common factor (GCF) of the terms in the expression. The expression has two terms: [tex]\(35x^2\)[/tex] and [tex]\(25\)[/tex].
2. Find the GCF: The coefficients of the terms are 35 and 25. The greatest common factor of 35 and 25 is 5.
3. Factor Out the GCF: Divide both terms of the expression by the GCF (5) and express the original expression as a product:
[tex]\[
35x^2 + 25 = 5(7x^2 + 5)
\][/tex]
4. Check for Further Factorization: After factoring out the GCF, check if the remaining expression inside the parentheses, [tex]\(7x^2 + 5\)[/tex], can be factored further. Since [tex]\(7x^2 + 5\)[/tex] is a sum of terms with no common factors and neither term can be factored further, this is the simplest form.
The completely factored form of the expression [tex]\(35x^2 + 25\)[/tex] is [tex]\(5(7x^2 + 5)\)[/tex].
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