Answer :
Using polynomial long division, we can then find the complete factorization as (x-5)(2x^2+5x-5).
To find the complete factorization of the polynomial 2x^3-5x^2-10x+25, we can use the Rational Root Theorem to find possible rational roots. By substituting the values, we find that x = 5 is a rational root. Using polynomial long division, we can then find the complete factorization as (x-5)(2x^2+5x-5).
To factorize the polynomial 2x3-5x2-10x+25, we can use the Rational Root Theorem to find possible rational roots. The possible rational roots of a polynomial are the factors of the constant term divided by the factors of the leading coefficient.
In this case, the constant term is 25 (factors: 1, 5, 25) and the leading coefficient is 2 (factors: 1, 2). So, the possible rational roots are ±1, ±5, ±25, ±1/2, and ±5/2.
By substituting these values into the polynomial, we find that the rational root x = 5 makes the polynomial equal to zero. Using polynomial long division, we can divide 2x3-5x2-10x+25 by x-5 to get the complete factorization of the polynomial as (x-5)(2x2+5x-5).
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