Question

For the polynomial below, 3 is a zero.

g(x)=x^3-7x^2+9x+9
Express g(x) as a product of linear factors

Answer 1

9514 1404 393

Answer:

g(x) = (x -3)(x -2+√7)(x -2 -√7)

Explanation:

Synthetic division can tell us the quadratic factor that remains when the factor (x-3) is divided out.

g(x) = (x -3)(x^2 -4x -3)

The quadratic is not factorable over integers. Its vertex form is ...

(x -2)^2 -7

so its roots are x = 2±√7.

That means the linear factorization of g(x) is ...

g(x) = (x -3)(x -2-√7)(x -2+√7)

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I find it easy to learn the vertex form of the quadratic factor by using a graphing calculator to show the graph of the quadratic.