Question
find the least common multiple of x^2 + x - 12 and x^2x - 15
Answers
GPT 3.5
To find the least common multiple of the given polynomials, first factor each polynomial to simplify the process.
Polynomial 1: x^2 + x - 12
This polynomial can be factored as:
(x + 4)(x - 3)
Polynomial 2: x^2x - 15
This polynomial can be factored as:
(x - 3)(x + 5)
Now, to find the least common multiple of these two polynomials, we need to find the product of the highest powers of all factors. In this case, the factors are (x + 4), (x - 3), and (x + 5).
Therefore, the least common multiple of x^2 + x - 12 and x^2x - 15 is:
(x + 4)(x - 3)(x + 5)
Polynomial 1: x^2 + x - 12
This polynomial can be factored as:
(x + 4)(x - 3)
Polynomial 2: x^2x - 15
This polynomial can be factored as:
(x - 3)(x + 5)
Now, to find the least common multiple of these two polynomials, we need to find the product of the highest powers of all factors. In this case, the factors are (x + 4), (x - 3), and (x + 5).
Therefore, the least common multiple of x^2 + x - 12 and x^2x - 15 is:
(x + 4)(x - 3)(x + 5)