For the polynomial below, 2 is a zero. g(x)=x^3-4x^2+9x-10. Express g(x) as a product of linear factors.

Answer 1

According to the question,

1. 2 is a zero of the polynomial
2. The polynomial is f(x) = x^3 - 4x^2 + 9x - 10

since x = 2 is a zero polynomial, (x-2) can be considered a factor.

By polynomial long division of f(x) by (x-2), we have;

1. f(x) = x³ - 4x² + 9x - 10 = (x-2)(x² - 2x + 5)

we therefore need to factorise the quadratic expression(x² - 2x + 5) using the quadratic formula:

1. x = (-b ± √(b² +4ac))/2a
2. where a = 1, b = -2, c =5

Therefore x = 1 + 2i and x = 1 - 2i

And the factors are:

1. (x - 2)(x -1 -2i)(x - 1 + 2i)