Step-by-step explanation:
Given f(x) = 2x³ + 9x² + 7x – 6
Also given that -3 is a root, which means (x+3) is a factor of f(x).
In order to find the other factors, we need to divide f(x) by (x-3)
or (2x³ + 9x² + 7x – 6) / (x-3)
you can either use long division or synthetic division to perform this division, either way, you will end up with :
(2x³ + 9x² + 7x – 6) / (x-3) = (2x² + 3x -2) which is also a factor of f(x)
Hence f(x) can be expressed
f(x) = 2x³ + 9x² + 7x – 6 = (x-3)(2x² + 3x -2)
We notice that for (2x² + 3x -2) you can further factor this using quadratic factoring (or your choice of method to solve quadratic equations).
By factoring, (2x² + 3x -2) = (2x-1) (x+2)
hence f(x) = (x-3)(2x² + 3x -2) = (x-3)(2x-1)(x+2)
