Question

question 8 of 10 given the trinomial $x^2 + bx - c$ where both the first sign is positive and the second sign is negative, the signs of the factors will be: a. cannot determine b. both positive c. one positive and one negative d. both negative

Explanation:

To factor the trinomial \(x^{2}+bx - c\) (where the constant term is \(-c\), meaning the product of the constant terms in the binomial factors is negative), and the middle term coefficient \(b\) comes from the sum of the constant terms in the binomial factors. For the product of two numbers to be negative, one number must be positive and the other negative (since positive \(\times\) negative = negative). And the sum of a positive and a negative number can result in the coefficient \(b\) (depending on their magnitudes, but the key here is the sign of the product of the constant terms in the factors). So, the two binomial factors will have one positive and one negative constant term.

Answer:

C. one positive and one negative