Question

Find a polynomial function of degree 3 with real coefficients that has the given zeros.

- 2, 3, -4

Answer 1

Polynomial functions' standard form is f(x)=ax^n+bx^n-1...+k

However, polynomials can also be written in intercept form

f(x)=(x-x1)(x-x2)(x-x3)...(x-xn) for roots/zeros x1,x2,x3,...,xn

With the three numbers that you have -2, 3, -4 you can write function

f(x)=(x-(-2))(x-3)(x-(-4))

Then you can simplify and distribute

f(x)=(x+2)(x-3)(x+4)

f(x)=(x^2-x-6)(x+4)

f(x)=x^3+3x^2-10x-24

Which would be the answer