Question

What is a polynomial function in standard form with zeros 1, 2, -3, and -1?

g(x)=x^4+x^3-7x^2-x+6

g(x)=x^4+x^3+7x^2-x+6

g(x)=x^4+x^3-7x^2-x-6

g(x)=x^4-x^3-7x^2-x+6

Answer 1

Answer: [tex] g(x)=x^4+x^3-7x^2-x+6[\tex]

Explanation:

Since, According to the question,

1, 2, - 3 and - 1 are zeros of the function g(x),

Also, function has the degree 4.

Thus, [tex]g(x) = (x-1)(x-2)(x+3)(x+1)[\tex]

[tex] g(x) = (x-1)(x-2)(x^2+4x+3)[\tex]

[tex] g(x) =(x-1)(x^3+4x^2+3x-2x^2-8x-6)[\tex]

[tex] g(x) =(x-1)(x^3+2x^2-5x-6)[\tex]

[tex] g(x) = x^4+x^3-7x^2-x+6[\tex]