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Answer :
To factor the expression [tex]\(70x^4 + 80x^2\)[/tex] completely, let's break it down into simpler steps:
1. Identify the Greatest Common Factor (GCF):
First, identify the common factor shared by the terms. Both terms, [tex]\(70x^4\)[/tex] and [tex]\(80x^2\)[/tex], can be divided by [tex]\(10x^2\)[/tex].
- The GCF of the numerical coefficients 70 and 80 is 10.
- The smallest power of [tex]\(x\)[/tex] common to both terms is [tex]\(x^2\)[/tex].
Therefore, the GCF of the entire expression is [tex]\(10x^2\)[/tex].
2. Factor out the GCF:
Divide each term by the GCF and place the GCF outside the parentheses:
[tex]\[
70x^4 + 80x^2 = 10x^2(7x^2) + 10x^2(8)
\][/tex]
Simplifying inside the parentheses, we get:
[tex]\[
10x^2(7x^2 + 8)
\][/tex]
3. Check for Further Factoring:
Now, we look inside the parentheses to see if [tex]\(7x^2 + 8\)[/tex] can be factored further. Both terms 7 and 8 are constants with no common factors other than 1, and [tex]\(7x^2\)[/tex] and 8 are not perfect squares or cubes, so this part is already fully factored.
Therefore, the completely factored form of the expression [tex]\(70x^4 + 80x^2\)[/tex] is:
[tex]\[
10x^2(7x^2 + 8)
\][/tex]
This is the final answer.
1. Identify the Greatest Common Factor (GCF):
First, identify the common factor shared by the terms. Both terms, [tex]\(70x^4\)[/tex] and [tex]\(80x^2\)[/tex], can be divided by [tex]\(10x^2\)[/tex].
- The GCF of the numerical coefficients 70 and 80 is 10.
- The smallest power of [tex]\(x\)[/tex] common to both terms is [tex]\(x^2\)[/tex].
Therefore, the GCF of the entire expression is [tex]\(10x^2\)[/tex].
2. Factor out the GCF:
Divide each term by the GCF and place the GCF outside the parentheses:
[tex]\[
70x^4 + 80x^2 = 10x^2(7x^2) + 10x^2(8)
\][/tex]
Simplifying inside the parentheses, we get:
[tex]\[
10x^2(7x^2 + 8)
\][/tex]
3. Check for Further Factoring:
Now, we look inside the parentheses to see if [tex]\(7x^2 + 8\)[/tex] can be factored further. Both terms 7 and 8 are constants with no common factors other than 1, and [tex]\(7x^2\)[/tex] and 8 are not perfect squares or cubes, so this part is already fully factored.
Therefore, the completely factored form of the expression [tex]\(70x^4 + 80x^2\)[/tex] is:
[tex]\[
10x^2(7x^2 + 8)
\][/tex]
This is the final answer.
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