Find a rational zero of the polynomial function and use it to find all the zeroes of the function. f(x)=x^3+2x^2-9x-18

Answer 1

Factor 1st 2 terms. x³ + 2x² = x²(× + 2)

Factor next 2 terms. -9x - 18 = -9(x + 2)

Notice they share the (x+ 2) factor,

So they total (x + 2)(x² -9). Factor x² - 9 as the difference of 2 squares, (x+ 3)(x-3)

Set to 0 to find roots

So we have (x + 2)(x + 3)(x - 3)= 0

One of the factors in ( ) must be 0.

Solve x + 2 = 0,......ans x = -2

Solve x + 3 = 0........ans x = -3

Solve x - 3 = 0..... ans x = 3

Roots are the three answers, -2, -3 and 3

Set to 0 to find roots.