Answer :
We start with the expression
[tex]$$20 x^4 + 45 x^5.$$[/tex]
Step 1: Find the greatest common factor (GCF).
- For the coefficients 20 and 45, the greatest common divisor is 5.
- For the variable part, the lower power of [tex]$x$[/tex] in both terms is [tex]$x^4$[/tex].
Thus, the GCF is [tex]$5x^4$[/tex].
Step 2: Factor out the GCF.
Divide each term by [tex]$5x^4$[/tex]:
- For the first term:
[tex]$$\frac{20x^4}{5x^4} = 4.$$[/tex]
- For the second term:
[tex]$$\frac{45x^5}{5x^4} = 9x.$$[/tex]
Step 3: Write the factored form.
After factoring out [tex]$5x^4$[/tex], the expression becomes:
[tex]$$5x^4(4 + 9x).$$[/tex]
Thus, the fully factored form is
[tex]$$5x^4(9x+4).$$[/tex]
[tex]$$20 x^4 + 45 x^5.$$[/tex]
Step 1: Find the greatest common factor (GCF).
- For the coefficients 20 and 45, the greatest common divisor is 5.
- For the variable part, the lower power of [tex]$x$[/tex] in both terms is [tex]$x^4$[/tex].
Thus, the GCF is [tex]$5x^4$[/tex].
Step 2: Factor out the GCF.
Divide each term by [tex]$5x^4$[/tex]:
- For the first term:
[tex]$$\frac{20x^4}{5x^4} = 4.$$[/tex]
- For the second term:
[tex]$$\frac{45x^5}{5x^4} = 9x.$$[/tex]
Step 3: Write the factored form.
After factoring out [tex]$5x^4$[/tex], the expression becomes:
[tex]$$5x^4(4 + 9x).$$[/tex]
Thus, the fully factored form is
[tex]$$5x^4(9x+4).$$[/tex]
