Question

Find a cubic function with the given zeros. (5 points)
-2, 5, -6

Answer 1

`\large\boxed{f(x)=x^3+3x^2-28x-60}`

Explanation:

If a, b and c are the zeros of a cubic function, then a function equation can have a form:

`f(x)=(x-a)(x-b)(x-c)`

We have the zeros: -2, 5 and -6. Then:

`f(x)=(x-(-2))(x-5)(x-(-6))=(x+2)(x-5)(x+6)`

Use FOIL (a + b)(c + d) = ac + ad + bc + bd:

`=\left[(x)(x)+(x)(-5)+(2)(x)+(2)(-5)\right](x+6)\\\\=(x^2-5x+2x-10)(x+6)\\\\=(x^2-3x-10)(x+6)\\\\=(x^2)(x)+(x^2)(6)+(-3x)(x)+(-3x)(6)+(-10)(x)+(-10)(6)\\\\=x^3+6x^2-3x^2-18x-10x-60\\\\=x^3+(6x^2-3x^2)+(-18x-10x)-60\\\\=x^3+3x^2-28x-60`