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Answer :
To factor the expression
[tex]$$9x^6 - 21x^9,$$[/tex]
follow these steps:
1. First, find the greatest common factor (GCF) of the coefficients. The coefficients are 9 and -21. The GCF of 9 and 21 is 3.
2. Next, look at the powers of [tex]$x$[/tex] in each term. The first term has [tex]$x^6$[/tex] and the second term has [tex]$x^9$[/tex]. The common factor is the smallest power, which is [tex]$x^6$[/tex].
3. Factor out [tex]$3x^6$[/tex] from each term. Divide each term by [tex]$3x^6$[/tex]:
- For the first term:
[tex]$$\frac{9x^6}{3x^6} = 3.$$[/tex]
- For the second term:
[tex]$$\frac{-21x^9}{3x^6} = -7x^3.$$[/tex]
4. Write the factored form by including the GCF and the remaining polynomial expression:
[tex]$$9x^6 - 21x^9 = 3x^6\left(3 - 7x^3\right).$$[/tex]
Thus, the expression factors as
[tex]$$\boxed{3x^6(3-7x^3)}.$$[/tex]
[tex]$$9x^6 - 21x^9,$$[/tex]
follow these steps:
1. First, find the greatest common factor (GCF) of the coefficients. The coefficients are 9 and -21. The GCF of 9 and 21 is 3.
2. Next, look at the powers of [tex]$x$[/tex] in each term. The first term has [tex]$x^6$[/tex] and the second term has [tex]$x^9$[/tex]. The common factor is the smallest power, which is [tex]$x^6$[/tex].
3. Factor out [tex]$3x^6$[/tex] from each term. Divide each term by [tex]$3x^6$[/tex]:
- For the first term:
[tex]$$\frac{9x^6}{3x^6} = 3.$$[/tex]
- For the second term:
[tex]$$\frac{-21x^9}{3x^6} = -7x^3.$$[/tex]
4. Write the factored form by including the GCF and the remaining polynomial expression:
[tex]$$9x^6 - 21x^9 = 3x^6\left(3 - 7x^3\right).$$[/tex]
Thus, the expression factors as
[tex]$$\boxed{3x^6(3-7x^3)}.$$[/tex]
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