Question
Factor the high-degree polynomial 6x^3+10x^2-9x-15 by grouping
Answers
GPT 3.5
To factor the polynomial 6x^3 + 10x^2 - 9x - 15 by grouping, we can group the terms and factor out the greatest common factor.
The first two terms, 6x^3 + 10x^2, have a common factor of 2x^2. Factoring out 2x^2 gives us:
2x^2(3x + 5)
The last two terms, -9x - 15, have a common factor of -3. Factoring out -3 gives us:
-3(3x + 5)
Now we can see that the terms in parentheses, (3x + 5), are the same in both groupings. We can factor it out to get the final factored form:
2x^2(3x + 5) - 3(3x + 5)
This can be further simplified as:
(2x^2 - 3)(3x + 5)
The first two terms, 6x^3 + 10x^2, have a common factor of 2x^2. Factoring out 2x^2 gives us:
2x^2(3x + 5)
The last two terms, -9x - 15, have a common factor of -3. Factoring out -3 gives us:
-3(3x + 5)
Now we can see that the terms in parentheses, (3x + 5), are the same in both groupings. We can factor it out to get the final factored form:
2x^2(3x + 5) - 3(3x + 5)
This can be further simplified as:
(2x^2 - 3)(3x + 5)