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Answer :
To factor the expression [tex]\(35x^2 + 63x^4\)[/tex] completely, you can follow these steps:
1. Identify the Greatest Common Factor (GCF):
- Look at the coefficients: 35 and 63. The GCF here is 7.
- For the variable part, both terms contain [tex]\(x^2\)[/tex]. So, the GCF for the variable part is [tex]\(x^2\)[/tex].
2. Factor Out the GCF:
- The GCF of the expression is [tex]\(7x^2\)[/tex].
- When you factor [tex]\(7x^2\)[/tex] out of each term in the expression, you divide each term by [tex]\(7x^2\)[/tex].
3. Rewrite Each Term:
- First term: [tex]\(35x^2\)[/tex] divided by [tex]\(7x^2\)[/tex] gives 5.
- Second term: [tex]\(63x^4\)[/tex] divided by [tex]\(7x^2\)[/tex] gives [tex]\(9x^2\)[/tex].
4. Write the Factored Expression:
- Combine the results of dividing each term by the GCF:
[tex]\[
35x^2 + 63x^4 = 7x^2(5 + 9x^2)
\][/tex]
The completely factored expression is:
[tex]\[
7x^2(9x^2 + 5)
\][/tex]
1. Identify the Greatest Common Factor (GCF):
- Look at the coefficients: 35 and 63. The GCF here is 7.
- For the variable part, both terms contain [tex]\(x^2\)[/tex]. So, the GCF for the variable part is [tex]\(x^2\)[/tex].
2. Factor Out the GCF:
- The GCF of the expression is [tex]\(7x^2\)[/tex].
- When you factor [tex]\(7x^2\)[/tex] out of each term in the expression, you divide each term by [tex]\(7x^2\)[/tex].
3. Rewrite Each Term:
- First term: [tex]\(35x^2\)[/tex] divided by [tex]\(7x^2\)[/tex] gives 5.
- Second term: [tex]\(63x^4\)[/tex] divided by [tex]\(7x^2\)[/tex] gives [tex]\(9x^2\)[/tex].
4. Write the Factored Expression:
- Combine the results of dividing each term by the GCF:
[tex]\[
35x^2 + 63x^4 = 7x^2(5 + 9x^2)
\][/tex]
The completely factored expression is:
[tex]\[
7x^2(9x^2 + 5)
\][/tex]
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