Question

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Write the simplest polynomial function using the three zeros given, where all coefficients are integers and the leading coefficient is positive. Enter your answers below.

Answer 1

Answer:
`f(x) = 2x^3-9x^2-23x+30`

Work Shown

`x = 6, \ x = 1, \ x = -5/2\\\\x-6 = 0, \ x-1 = 0, \ 2x+5 = 0\\\\(x-6)(x-1)(2x+5) = 0\\\\(x^2-1x-6x+6)(2x+5) = 0\\\\(x^2-7x+6)(2x+5) = 0\\\\2x(x^2-7x+6)+5(x^2-7x+6) = 0\\\\(2x^3-14x^2+12x)+(5x^2-35x+30) = 0\\\\2x^3+(-14x^2+5x^2)+(12x-35x)+30 = 0\\\\2x^3-9x^2-23x+30 = 0\\\\`

Therefore, the polynomial function
`f(x) = 2x^3-9x^2-23x+30` has roots x = 6, x = 1, x = -5/2. It is considered "simplest" because the GCF of the coefficients is 1.