Find a pelynomial with integer coefficients that satisfies the given conditions, \[ P(x)=x^{2}-5 x+6 \text { has degre } 2 \text { and zoros? } \]

To find a polynomial with integer coefficients that has a degree of 2 and the same roots as the polynomial \( P(x) = x^2 - 5x + 6 \), we first need to identify the roots of \( P(x) \). By factoring, we find: \[ P(x) = (x - 2)(x - 3) \] This shows that the roots are \( x = 2 \) and \( x = 3 \). Any polynomial with the same roots can be formed by multiplying \( (x - 2)(x - 3) \) by any non-zero integer (to keep the coefficients as integers). Hence, we can write: \[ Q(x) = k(x - 2)(x - 3) \] where \( k \) is any non-zero integer. For simplicity, if we take \( k = 1 \), we have: \[ Q(x) = (x - 2)(x - 3) = x^2 - 5x + 6 \] Thus, the polynomial we are looking for, that has integer coefficients and the required properties, is: \[ Q(x) = x^2 - 5x + 6 \] This fulfills the criteria as it is of degree 2 and has roots at \( x = 2 \) and \( x = 3 \).