Answer :
We start with the expression
[tex]$$15x^4 - 45x^3.$$[/tex]
Step 1: Identify the Greatest Common Factor (GCF)
Look at the two terms:
- The first term is [tex]$15x^4$[/tex].
- The second term is [tex]$45x^3$[/tex].
The common numerical factor is [tex]$15$[/tex], and the variable part common to both terms is [tex]$x^3$[/tex] (since [tex]$x^4 = x^3 \cdot x$[/tex] and [tex]$x^3$[/tex] is present in both terms).
Thus, the GCF is [tex]$15x^3$[/tex].
Step 2: Factor Out the GCF
Divide each term by the GCF [tex]$15x^3$[/tex]:
- For [tex]$15x^4$[/tex]:
[tex]$$\frac{15x^4}{15x^3} = x.$$[/tex]
- For [tex]$-45x^3$[/tex]:
[tex]$$\frac{-45x^3}{15x^3} = -3.$$[/tex]
Step 3: Write the Factored Expression
After factoring out the GCF, the expression can be written as:
[tex]$$15x^4 - 45x^3 = 15x^3\left(x - 3\right).$$[/tex]
Final Answer:
[tex]$$15x^3(x-3).$$[/tex]
[tex]$$15x^4 - 45x^3.$$[/tex]
Step 1: Identify the Greatest Common Factor (GCF)
Look at the two terms:
- The first term is [tex]$15x^4$[/tex].
- The second term is [tex]$45x^3$[/tex].
The common numerical factor is [tex]$15$[/tex], and the variable part common to both terms is [tex]$x^3$[/tex] (since [tex]$x^4 = x^3 \cdot x$[/tex] and [tex]$x^3$[/tex] is present in both terms).
Thus, the GCF is [tex]$15x^3$[/tex].
Step 2: Factor Out the GCF
Divide each term by the GCF [tex]$15x^3$[/tex]:
- For [tex]$15x^4$[/tex]:
[tex]$$\frac{15x^4}{15x^3} = x.$$[/tex]
- For [tex]$-45x^3$[/tex]:
[tex]$$\frac{-45x^3}{15x^3} = -3.$$[/tex]
Step 3: Write the Factored Expression
After factoring out the GCF, the expression can be written as:
[tex]$$15x^4 - 45x^3 = 15x^3\left(x - 3\right).$$[/tex]
Final Answer:
[tex]$$15x^3(x-3).$$[/tex]
