Question

question 10 of 10
when the factors of a trinomial are (x - p) and (x - q) then the constant term of the trinomial is:
a. the quotient of -p and -q
b. the difference of -p and -q
c. the sum of -p and -q
d. the product of -p and -q

Explanation:

Step1: Expand the factors

We have the factors \((x - p)\) and \((x - q)\). To find the trinomial, we multiply these two binomials using the distributive property (FOIL method).

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Step2: Identify the constant term

In the trinomial \(x^2 - (p + q)x + pq\), the constant term is \(pq\). Now, let's analyze \(pq\) in terms of \(-p\) and \(-q\). We know that \((-p)\times(-q)=pq\) (because the product of two negative numbers is positive). So the constant term is the product of \(-p\) and \(-q\).

Answer:

D. The product of -p and -q