Answer :
Sure, let's factor out the negative sign along with the greatest common factor (GCF) for the expression [tex]\(-4x^3 + 28x^2 - 20x\)[/tex].
### Step-by-step Solution:
1. Identify the GCF of the coefficients:
- The coefficients of the terms are [tex]\(-4\)[/tex], [tex]\(28\)[/tex], and [tex]\(-20\)[/tex].
- The GCF of [tex]\(-4\)[/tex], [tex]\(28\)[/tex], and [tex]\(-20\)[/tex] is [tex]\(4\)[/tex].
2. Factor out the negative sign:
- We can factor out [tex]\(-1\)[/tex] from the expression to make it easier to work with:
[tex]\[
-1 \times (4x^3 - 28x^2 + 20x)
\][/tex]
3. Factor out the GCF (which is 4) from the expression inside the parentheses:
- We have:
[tex]\[
4x^3 - 28x^2 + 20x
\][/tex]
- Each term has a [tex]\(4x\)[/tex] that can be factored out:
[tex]\[
4x(x^2 - 7x + 5)
\][/tex]
4. Combine the factored parts along with the negative sign:
- We previously factored out a [tex]\(-1\)[/tex], so the expression becomes:
[tex]\[
-4x(x^2 - 7x + 5)
\][/tex]
Therefore, the expression [tex]\(-4x^3 + 28x^2 - 20x\)[/tex] is factored as:
[tex]\[
-4x(x^2 - 7x + 5)
\][/tex]
### Step-by-step Solution:
1. Identify the GCF of the coefficients:
- The coefficients of the terms are [tex]\(-4\)[/tex], [tex]\(28\)[/tex], and [tex]\(-20\)[/tex].
- The GCF of [tex]\(-4\)[/tex], [tex]\(28\)[/tex], and [tex]\(-20\)[/tex] is [tex]\(4\)[/tex].
2. Factor out the negative sign:
- We can factor out [tex]\(-1\)[/tex] from the expression to make it easier to work with:
[tex]\[
-1 \times (4x^3 - 28x^2 + 20x)
\][/tex]
3. Factor out the GCF (which is 4) from the expression inside the parentheses:
- We have:
[tex]\[
4x^3 - 28x^2 + 20x
\][/tex]
- Each term has a [tex]\(4x\)[/tex] that can be factored out:
[tex]\[
4x(x^2 - 7x + 5)
\][/tex]
4. Combine the factored parts along with the negative sign:
- We previously factored out a [tex]\(-1\)[/tex], so the expression becomes:
[tex]\[
-4x(x^2 - 7x + 5)
\][/tex]
Therefore, the expression [tex]\(-4x^3 + 28x^2 - 20x\)[/tex] is factored as:
[tex]\[
-4x(x^2 - 7x + 5)
\][/tex]
