Question

f(x)= -3^2+2x-9.....Factor f(x) into a product of linear terms.

Answer 1

Is your problem copied correctly?
Should it be \(f(x) = -3x^2 + 2x - 9\) ?

I don't like to work with a negative leading coefficient, so I'll start by factoring -1.

\(f(x) = -3x^2 + 2x - 9\)

\(f(x) = -1(3x^2 - 2x + 9)\)

We need to factor a quadratic trinomial whose leading coefficient is not 1.
The trinomial is of the form \(ax^2 + bx + c\).
We can use the \(ac\) method.

1. Multiply \(ac\): \(3 \times 9 = 27\)
2. Factor \(ac\) into two factors whose sum is \(b\): there are no two such numbers, so this trinomial is not factorable.