Answer :
Let's go through the process of factoring the expression [tex]\(-45 - 50x^4\)[/tex] completely.
1. Identify a Common Factor:
First, look for any common factors in the terms of the expression. Here, we notice that both [tex]\(-45\)[/tex] and [tex]\(-50\)[/tex] are divisible by [tex]\(-5\)[/tex].
2. Factor Out the Greatest Common Factor (GCF):
Factoring [tex]\(-5\)[/tex] from the expression gives:
[tex]\[
-45 - 50x^4 = -5(9 + 10x^4)
\][/tex]
3. Check for Further Factoring:
Examine the expression inside the parentheses, [tex]\(9 + 10x^4\)[/tex], to see if it can be factored further. In this case, [tex]\(9 + 10x^4\)[/tex] does not factor into simpler polynomials with rational coefficients.
Thus, the completely factored form of the expression [tex]\(-45 - 50x^4\)[/tex] is:
[tex]\[
-5(9 + 10x^4)
\][/tex]
1. Identify a Common Factor:
First, look for any common factors in the terms of the expression. Here, we notice that both [tex]\(-45\)[/tex] and [tex]\(-50\)[/tex] are divisible by [tex]\(-5\)[/tex].
2. Factor Out the Greatest Common Factor (GCF):
Factoring [tex]\(-5\)[/tex] from the expression gives:
[tex]\[
-45 - 50x^4 = -5(9 + 10x^4)
\][/tex]
3. Check for Further Factoring:
Examine the expression inside the parentheses, [tex]\(9 + 10x^4\)[/tex], to see if it can be factored further. In this case, [tex]\(9 + 10x^4\)[/tex] does not factor into simpler polynomials with rational coefficients.
Thus, the completely factored form of the expression [tex]\(-45 - 50x^4\)[/tex] is:
[tex]\[
-5(9 + 10x^4)
\][/tex]
