To factor the quadratic expression x^2 + 3x - 10 as (x+p)(x+q), we need to find values for p and q that satisfy the equation. The general form of a quadratic expression is ax^2 + bx + c, where a, b, and c are constants. In this case, a = 1, b = 3, and c = -10. To find the values of p and q, we need to consider the following: 1. The product of p and q should be equal to the constant term c. In this case, c = -10. So, we need to find two numbers that multiply to -10. 2. The sum of p and q should be equal to the coefficient of the middle term b. In this case, b = 3. So, we need to find two numbers that add up to 3. Now, let's consider the answer choices:
A. 2 and -5: The product of 2 and -5 is -10, which matches the constant term. The sum of 2 and -5 is -3, which matches the coefficient of the middle term. Therefore, (x+2)(x-5) is a correct factorization.
B. -1 and 10: The product of -1 and 10 is -10, which matches the constant term. The sum of -1 and 10 is 9, which does not match the coefficient of the middle term. Therefore, (x-1)(x+10) is not a correct factorization.
C. -2 and 5: The product of -2 and 5 is -10, which matches the constant term. The sum of -2 and 5 is 3, which matches the coefficient of the middle term. Therefore, (x-2)(x+5) is a correct factorization.
D. 1 and -10: The product of 1 and -10 is -10, which matches the constant term. The sum of 1 and -10 is -9, which does not match the coefficient of the middle term. Therefore, (x+1)(x-10) is not a correct factorization.
In conclusion, the values of p and q that should be used to factor x^2 + 3x - 10 as (x+p)(x+q) are 2 and -5, as shown in answer choice A.
