Question

I need to know the constant term of this problem

Answer 1

Given: The polynominal below where m is the unknown

`3x^3-5x^2-47x+m`

To Determine: The value of the unknown when (x+3) is a factor

Solution

If (x+3) is a factor, then its zero will give the zero of the given polynomial. Therefore

`\begin{gathered} x=3=0 \\ x=-3 \end{gathered}`
`3(-3)^3-5(-3)^2-47(-3)+m=0`
`\begin{gathered} 3(-27)-5(9)+141+m=0 \\ -81-45+141+m=0 \\ -126+141+m=0 \\ 15+m=0 \\ m=-15 \end{gathered}`

Hence, the empty space is -15