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Answer :
To factor the expression
[tex]$$18x^4 - 21x^3,$$[/tex]
we can follow these steps:
1. Identify the common factors:
Look at the coefficients [tex]$18$[/tex] and [tex]$-21$[/tex]. Both have a common factor of [tex]$3$[/tex].
Also, the terms contain the variable [tex]$x$[/tex], and the smallest power of [tex]$x$[/tex] present in both terms is [tex]$x^3$[/tex].
Therefore, we can factor out [tex]$3x^3$[/tex].
2. Factor out the common factor:
Divide each term by [tex]$3x^3$[/tex]:
- For the first term:
[tex]$$\frac{18x^4}{3x^3} = 6x.$$[/tex]
- For the second term:
[tex]$$\frac{-21x^3}{3x^3} = -7.$$[/tex]
3. Write the factored form:
After factoring out [tex]$3x^3$[/tex], the expression becomes:
[tex]$$18x^4 - 21x^3 = 3x^3(6x - 7).$$[/tex]
Thus, the fully factored form of the polynomial is
[tex]$$\boxed{3x^3(6x - 7)}.$$[/tex]
[tex]$$18x^4 - 21x^3,$$[/tex]
we can follow these steps:
1. Identify the common factors:
Look at the coefficients [tex]$18$[/tex] and [tex]$-21$[/tex]. Both have a common factor of [tex]$3$[/tex].
Also, the terms contain the variable [tex]$x$[/tex], and the smallest power of [tex]$x$[/tex] present in both terms is [tex]$x^3$[/tex].
Therefore, we can factor out [tex]$3x^3$[/tex].
2. Factor out the common factor:
Divide each term by [tex]$3x^3$[/tex]:
- For the first term:
[tex]$$\frac{18x^4}{3x^3} = 6x.$$[/tex]
- For the second term:
[tex]$$\frac{-21x^3}{3x^3} = -7.$$[/tex]
3. Write the factored form:
After factoring out [tex]$3x^3$[/tex], the expression becomes:
[tex]$$18x^4 - 21x^3 = 3x^3(6x - 7).$$[/tex]
Thus, the fully factored form of the polynomial is
[tex]$$\boxed{3x^3(6x - 7)}.$$[/tex]
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