When the factors of a trinomial are (x - p) and (x - q) then the coefficient of the x-term in the trinomial is:A.The quotient of -p and -qB.The difference of -p and -qC.The product of -p and -qD.The sum of -p and -qSUBMITarrow_backPREVIOUS
Question
When the factors of a trinomial are (x - p) and (x - q) then the coefficient of the x-term in the trinomial is:A.The quotient of -p and -qB.The difference of -p and -qC.The product of -p and -qD.The sum of -p and -qSUBMITarrow_backPREVIOUS
Solution
The correct answer is D. The sum of -p and -q.
Here's why:
When you multiply the factors of a trinomial, you get the trinomial itself. So, if the factors are (x - p) and (x - q), you multiply them to get the trinomial:
(x - p)(x - q) = x^2 - (p + q)x + pq
The coefficient of the x-term in the trinomial is the number that multiplies x, which in this case is -(p + q). But since p and q are subtracted in the factors, they become negative in the trinomial. So, the coefficient of the x-term is the sum of -p and -q.
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