Answer :
Final answer:
The greatest common factor of the expression 21x^7 - 35x^5 -14x^3 is 7x^3. After removing the greatest common factor, the simplified expression is 7x^3(3x^4 - 5x^2 - 2).
Explanation:
To remove the greatest common factor, you first need to identify what the common factor of all the terms in the expression is. In this case, the common factor of 21x7, -35x5, and -14x3 is 7x3.
Then we divide each term by the greatest common factor:
- 21x7 / 7x3 = 3x4
- -35x5 / 7x3 = -5x2
- -14x3 / 7x3 = -2
So the expression after removing the greatest common factor is: 7x3(3x4 - 5x2 - 2)
You can check your answer by multiplying the factor back:
7x3 * 3x4 = 21x7
7x3 * -5x2 = -35x5
7x3 * -2 = -14x3
This checks out with the original expression.
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