Answer :

To factor the given expression completely, follow these steps:

The expression is:
[tex]\[
-x^6 y^3 z - 23 x^4 y^5 z^2
\][/tex]

1. Identify Common Factors:
Look for common factors in both terms. The terms are:
- [tex]\(-x^6 y^3 z\)[/tex]
- [tex]\(-23 x^4 y^5 z^2\)[/tex]

Both terms have the following common factors:
- [tex]\(x^4\)[/tex] (as [tex]\(x^6\)[/tex] contains [tex]\(x^4\)[/tex] and [tex]\(x^4\)[/tex] is already present)
- [tex]\(y^3\)[/tex] (since the first term has [tex]\(y^3\)[/tex] and the second term has [tex]\(y^5\)[/tex])
- [tex]\(z\)[/tex] (common in both terms)

So, the greatest common factor (GCF) is [tex]\(x^4 y^3 z\)[/tex].

2. Factor Out the GCF:
Divide each term by the GCF [tex]\(x^4 y^3 z\)[/tex]:

- For [tex]\(-x^6 y^3 z\)[/tex]:
[tex]\[
\frac{-x^6 y^3 z}{x^4 y^3 z} = -x^2
\][/tex]

- For [tex]\(-23 x^4 y^5 z^2\)[/tex]:
[tex]\[
\frac{-23 x^4 y^5 z^2}{x^4 y^3 z} = -23y^2 z
\][/tex]

3. Write the Factored Form:
After factoring out the GCF, the expression becomes:
[tex]\[
x^4 y^3 z \left(-x^2 - 23y^2 z\right)
\][/tex]

To make it look neat, rearrange the terms:
[tex]\[
-x^4 y^3 z \left(x^2 + 23y^2 z\right)
\][/tex]

Thus, the expression [tex]\(-x^6 y^3 z - 23 x^4 y^5 z^2\)[/tex] factors completely as:
[tex]\[
-x^4 y^3 z \left(x^2 + 23y^2 z\right)
\][/tex]

Other Questions