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I need to know the constant term of this problem

I Need To Know The Constant Term Of This Problem class=

Sagot :

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

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