Answer :
Final answer:
The factored form of the polynomial P(x)=6x^5+23x^4−24x^3−113x^2+24x+36 cannot be determined without finding the roots of the polynomial.
Explanation:
To factor the polynomial P(x)=6x^5+23x^4−24x^3−113x^2+24x+36, we need to find its roots or zeros. Unfortunately, there is no simple method to find the roots of a polynomial of degree 5. However, we can use numerical methods or technology to approximate the roots.
Once we have the roots, we can express the polynomial as a product of linear factors. For example, if we find that the roots are x=1, x=2, and x=-3, then the factored form of P(x) would be:
P(x) = (x-1)(x-2)(x+3)(ax^2+bx+c)
Where (ax^2+bx+c) represents the quadratic factor that remains after factoring out the linear factors.
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