Answer :
To factor the expression [tex]\(70x^4 + 80x^2\)[/tex] completely, follow these steps:
1. Identify the Greatest Common Factor (GCF):
- First, look for the largest number that divides both coefficients. The coefficients are 70 and 80.
- The GCF of 70 and 80 is 10.
- Next, look for the smallest power of [tex]\(x\)[/tex] present in both terms. Here, the smallest power of [tex]\(x\)[/tex] is [tex]\(x^2\)[/tex].
2. Factor out the GCF:
- Once you have identified the GCF, which is [tex]\(10x^2\)[/tex], you can factor it out of each term in the expression.
- This means rewriting the expression [tex]\(70x^4 + 80x^2\)[/tex] as:
[tex]\[
70x^4 + 80x^2 = 10x^2(7x^2 + 8)
\][/tex]
3. Simplify the Expression Inside the Parentheses:
- Now, look at the expression inside the parentheses, [tex]\(7x^2 + 8\)[/tex], to see if it can be factored further.
- Since 7 is a prime number and 8 does not share any common factors with 7 other than 1, [tex]\(7x^2 + 8\)[/tex] cannot be factored further with integer coefficients.
4. Write the Completely Factored Expression:
- The completely factored form of the expression is:
[tex]\[
10x^2(7x^2 + 8)
\][/tex]
This is the completely factored version of the original expression [tex]\(70x^4 + 80x^2\)[/tex].
1. Identify the Greatest Common Factor (GCF):
- First, look for the largest number that divides both coefficients. The coefficients are 70 and 80.
- The GCF of 70 and 80 is 10.
- Next, look for the smallest power of [tex]\(x\)[/tex] present in both terms. Here, the smallest power of [tex]\(x\)[/tex] is [tex]\(x^2\)[/tex].
2. Factor out the GCF:
- Once you have identified the GCF, which is [tex]\(10x^2\)[/tex], you can factor it out of each term in the expression.
- This means rewriting the expression [tex]\(70x^4 + 80x^2\)[/tex] as:
[tex]\[
70x^4 + 80x^2 = 10x^2(7x^2 + 8)
\][/tex]
3. Simplify the Expression Inside the Parentheses:
- Now, look at the expression inside the parentheses, [tex]\(7x^2 + 8\)[/tex], to see if it can be factored further.
- Since 7 is a prime number and 8 does not share any common factors with 7 other than 1, [tex]\(7x^2 + 8\)[/tex] cannot be factored further with integer coefficients.
4. Write the Completely Factored Expression:
- The completely factored form of the expression is:
[tex]\[
10x^2(7x^2 + 8)
\][/tex]
This is the completely factored version of the original expression [tex]\(70x^4 + 80x^2\)[/tex].
