College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Factor the expression completely.

[tex]\[ 70x^4 + 80x^2 \] [/tex]

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.