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6x^7+3x^4-9x^3 factor

User JustnpT
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1 Answer

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Answer:


3x^3(x-1)(2x^3+2x^2+2x+3)

Explanation:

We can start by factoring out x³ because it's the greatest factor of every term:


6x^7+3x^4-9x^3=x^3(6x^4+3x-9)

Next, notice that each coefficient is divisible by 3, so this can be factored out as well:


x^3(6x^4+3x-9)=3x^3(2x^4+x-3)

While it may not look like we can factor out 2x⁴+x-3, we actually can! Notice the following:


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)

By grouping, we were able to condense this factor. Thus:


6x^7+3x^4-9x^3=\bf{3x^3(x-1)(2x^3+2x^2+2x+3)}

User Elprup
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