The values of p and q are D. 2 and -5
To factor the quadratic expression $x^2 + 3x - 10$ as $(x + p)(x + q)$, we need to find the values of $p$ and $q$ such that $p + q = 3$ and $pq = -10$. From the given table, we can see that the only pair of values that satisfy these conditions is $p = 2$ and $q = -5$, since $p + q = 2 + (-5) = -3$ and $pq = 2 \cdot (-5) = -10$. Therefore, we can write:
x²+3x−10=(x+2)(x−5)
To check that this is the correct factorization, we can use the distributive property:
(x+2)(x−5)=x(x−5)+2(x−5) = x²−5x+2x−10=x² −3x−10
which is the original expression. Therefore, the values of $p$ and $q$ that should be used to factor $x^2 + 3x - 10$ as $(x + p)(x + q)$ are $p = 2$ and $q = -5$.
Therefore, the correct answer is: D. 2 and -5