Answer :
Answer:
[tex]3x^3(x-1)(2x^3+2x^2+2x+3)[/tex]
Step-by-step explanation:
We can start by factoring out x³ because it's the greatest factor of every term:
[tex]6x^7+3x^4-9x^3=x^3(6x^4+3x-9)[/tex]
Next, notice that each coefficient is divisible by 3, so this can be factored out as well:
[tex]x^3(6x^4+3x-9)=3x^3(2x^4+x-3)[/tex]
While it may not look like we can factor out 2x⁴+x-3, we actually can! Notice the following:
[tex]2x^4+x-3=(2x^4+2x^3+2x^2+3x)+(-2x^3-2x^2-2x-3)=x(2x^3+2x^2+2x+3)-1(2x^3-2x^2+2x+3)=(x-1)(2x^3+2x^2+2x+3)[/tex]
By grouping, we were able to condense this factor. Thus:
[tex]6x^7+3x^4-9x^3=\bf{3x^3(x-1)(2x^3+2x^2+2x+3)}[/tex]
