To factor the polynomial [tex]\(14xz - 12z\)[/tex] completely, follow these steps:
1. Identify the common factors in the terms:
- The terms are [tex]\(14xz\)[/tex] and [tex]\(12z\)[/tex].
- Look at the coefficients [tex]\(14\)[/tex] and [tex]\(12\)[/tex]. The greatest common factor (GCF) of [tex]\(14\)[/tex] and [tex]\(12\)[/tex] is [tex]\(2\)[/tex].
- Both terms also contain the variable [tex]\(z\)[/tex].
2. Factor out the GCF from each term:
- Since the GCF of the coefficients is [tex]\(2\)[/tex] and both terms contain [tex]\(z\)[/tex], the overall GCF we can factor out is [tex]\(2z\)[/tex].
3. Express each term as a product of the GCF and another factor:
- [tex]\(14xz\)[/tex] can be written as [tex]\((2z) \times (7x)\)[/tex].
- [tex]\(12z\)[/tex] can be written as [tex]\((2z) \times 6\)[/tex].
4. Factor the polynomial by taking out the GCF:
- When we factor [tex]\(2z\)[/tex] out of each term, we get:
[tex]\[
14xz - 12z = 2z(7x) - 2z(6)
\][/tex]
- This can be simplified as:
[tex]\[
2z(7x - 6)
\][/tex]
Therefore, the polynomial [tex]\(14xz - 12z\)[/tex] factored completely is:
[tex]\[
2z(7x - 6)
\][/tex]
