Given: The polynominal below where m is the unknown
[tex]3x^3-5x^2-47x+m[/tex]
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
[tex]\begin{gathered} x=3=0 \\ x=-3 \end{gathered}[/tex][tex]3(-3)^3-5(-3)^2-47(-3)+m=0[/tex][tex]\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}[/tex]
Hence, the empty space is -15
