12. One of the factors of the polynomial 2x^3-5x^2+6x-15 is 2x-5 Which of the following expressions is the other factor of the given polynomial? 2x^2-3 x(3-x) 3-2x^2 x^2+3

To find the other factor of the polynomial $2x^{3}-5x^{2}+6x-15$, we can use polynomial division or synthetic division.<br /><br />Let's use synthetic division to divide the polynomial by the factor $2x-5$.<br /><br />Step 1: Write down the coefficients of the polynomial: 2, -5, 6, -15.<br /><br />Step 2: Write down the zero of the factor $2x-5$, which is $x=\frac{5}{2}$.<br /><br />Step 3: Perform synthetic division:<br /><br />```<br /> 2 -5 6 -15<br /> 5/2<br /> 2 0 3 0<br />```<br /><br />Step 4: The quotient is $2x^{2}+3$.<br /><br />Therefore, the other factor of the given polynomial is $2x^{2}+3$.<br /><br />So, the correct answer is $2x^{2}-3$.