Certainly! Let's factor the given expression step-by-step:
Given expression:
[tex]\[ 3x + xz - 51y - 17yz \][/tex]
1. Identify common factors in pairs:
First, group the terms to make factoring easier:
[tex]\[ 3x + xz - 51y - 17yz \][/tex]
2. Factor out the greatest common factor (GCF) from each pair:
- For the first pair, [tex]\(3x + xz\)[/tex], factor out [tex]\(x\)[/tex]:
[tex]\[ x(3 + z) \][/tex]
- For the second pair, [tex]\(-51y - 17yz\)[/tex], factor out [tex]\(-17y\)[/tex]:
[tex]\[ -17y(3 + z) \][/tex]
Now, rewrite the expression with the factored pairs:
[tex]\[ x(3 + z) - 17y(3 + z) \][/tex]
3. Factor out the common binomial factor:
Notice that both terms have a common factor of [tex]\((3 + z)\)[/tex]:
[tex]\[ (3 + z)(x - 17y) \][/tex]
4. Simplify and reorder the factors for clarity:
Arrange the factors in a standard way:
[tex]\[ (x - 17y)(z + 3) \][/tex]
So, the factored form of the expression [tex]\( 3x + xz - 51y - 17yz \)[/tex] is:
[tex]\[ (x - 17y)(z + 3) \][/tex]
This concludes our factoring process.
