# Order of operations in evaluating a polynomial

I have the following function $$f(x) = 3x^3 - 5x^2 - 4x + 4.$$

I would like to find the value of $f(x)$ when $x = -3$.

I have ordered the equation in the following way. $$f(-3) = (3 \times -3^3) - (5 \times -3^2) - (4 \times -3) + 4 = -28.$$

Can anyone tell me if the following syntax is correct and if not, where have I gone wrong.

Many Thanks.

• Is your function supposed to be $f(x) = 3x^3 -5x^2-4x+4$? – Arturo Magidin Feb 23 '11 at 20:53
• yes correct thats exactly how it appears on my paper. – cocacola09 Feb 23 '11 at 20:54
• You wrote $f(x)=3x^2-...$ (squared, not cubed). That's why I asked. – Arturo Magidin Feb 23 '11 at 20:56

When you write $5*-3^2$, the precedence of operations means that you first compute $3^2$, then you multiply the result by $-1$, then you multiply the entire thing by $5$. This is not what you want.
Don't be scared of parentheses! The best way to write this, if you want to insist on putting the $*$ in it (we normally just write multiplication by juxtaposition) would be: $$f(-3) = (3*(-3)^3) - (5*(-3)^2) - (4*(-3)) + 4.$$ More succinctly, you can write it as: $$f(-3) = 3(-3)^3 - 5(-3)^2 - 4(-3) + 4.$$ By the precedence order, you would first compute the exponentials, then the products, then the sums.
That said, I don't think you computed $f(-3)$ correctly.