Question

For the polynomial below, -3 is a zero.

g(x) = x³ + 9x² + 24x + 18

Express g (x) as a product of linear factors.

Answer 1

To express the polynomial g(x) = x³ + 9x² + 24x + 18 as a product of linear factors, we divide by the given zero -3 using synthetic division.

Step-by-step explanation:

To express the polynomial g(x) = x³ + 9x² + 24x + 18 as a product of linear factors, we need to find all the possible zeros of the polynomial.

Since -3 is given as a zero, we can divide the polynomial by (x + 3) using synthetic division to find the quotient.

The quotient obtained is x² + 6x + 6.

Thus, g(x) = (x + 3)(x² + 6x + 6).