Answer :
Sure, let's factor the expression [tex]\(-45 - 50x^4\)[/tex] completely, step-by-step.
1. Determine the Greatest Common Factor (GCF):
Look at the coefficients of the terms [tex]\(-45\)[/tex] and [tex]\(-50x^4\)[/tex]. The GCF of [tex]\(45\)[/tex] and [tex]\(50\)[/tex] is [tex]\(5\)[/tex]. Since both terms are negative, we will factor out a [tex]\(-5\)[/tex].
2. Factor out the GCF:
Divide each term by [tex]\(-5\)[/tex]:
[tex]\[
-45 \div -5 = 9
\][/tex]
[tex]\[
-50x^4 \div -5 = 10x^4
\][/tex]
So, after factoring out [tex]\(-5\)[/tex], the expression becomes:
[tex]\[
-5(9 + 10x^4)
\][/tex]
3. Check for Further Factorization:
Look at the expression inside the parentheses: [tex]\(9 + 10x^4\)[/tex].
- The term [tex]\(9\)[/tex] is a perfect square. However, this expression is a sum, not a difference of squares, so it cannot be factored further using real numbers.
Thus, the completely factored form of the expression is:
[tex]\[
-5(9 + 10x^4)
\][/tex]
That's the final answer!
1. Determine the Greatest Common Factor (GCF):
Look at the coefficients of the terms [tex]\(-45\)[/tex] and [tex]\(-50x^4\)[/tex]. The GCF of [tex]\(45\)[/tex] and [tex]\(50\)[/tex] is [tex]\(5\)[/tex]. Since both terms are negative, we will factor out a [tex]\(-5\)[/tex].
2. Factor out the GCF:
Divide each term by [tex]\(-5\)[/tex]:
[tex]\[
-45 \div -5 = 9
\][/tex]
[tex]\[
-50x^4 \div -5 = 10x^4
\][/tex]
So, after factoring out [tex]\(-5\)[/tex], the expression becomes:
[tex]\[
-5(9 + 10x^4)
\][/tex]
3. Check for Further Factorization:
Look at the expression inside the parentheses: [tex]\(9 + 10x^4\)[/tex].
- The term [tex]\(9\)[/tex] is a perfect square. However, this expression is a sum, not a difference of squares, so it cannot be factored further using real numbers.
Thus, the completely factored form of the expression is:
[tex]\[
-5(9 + 10x^4)
\][/tex]
That's the final answer!
