Question

pick the expression that matches this description:
a trinomial with a leading coefficient of 3 and a constant term of -5
choose 1 answer:
a ( 3m^2 - 5 )
b ( 3m^2 - 5m + 1 )
c ( -5m^2 + 4m + 3 )
d ( 3m^2 + m - 5 )

Explanation:

Step1: Define trinomial check

A trinomial has 3 distinct terms.

• Option A: $3m^2 - 5$ has 2 terms → reject.
• Option B: $3m^2 -5m +1$ has 3 terms → keep.
• Option C: $-5m^2 +4m +3$ has 3 terms → keep.
• Option D: $3m^2 +m -5$ has 3 terms → keep.

Step2: Check leading coefficient=3

Leading coefficient is coefficient of highest degree term.

• Option B: Leading coefficient $3$ → keep.
• Option C: Leading coefficient $-5$ → reject.
• Option D: Leading coefficient $3$ → keep.

Step3: Check constant term=-5

Constant term is term without variable.

• Option B: Constant term $1$ → reject.
• Option D: Constant term $-5$ → keep.

Answer:

D. $3m^2 + m - 5$