Simple Calculus Function I am doing a course in calculus and I was given this problem :
Given that $f(x)=3x^4−6x^3+4x^2−7x+3$, evaluate $f(−2)$.
The answer is meant to be 129 according to the tutor, but no matter how many times I try and work it out I can't see how they got that answer.
 A: Observe the magic of color:$$f(\color{#C00}{x}) = 3\color{#C00}{x}^4 - 6\color{#C00}{x}^3  + 4\color{#C00}{x}^2 - 7\color{#C00}{x} + 3$$Now, we essentially have to replace our colored expressions with numbers.$$f(-2) = 3(-2)^4 - 6(-2)^3 + 4(-2)^3 - 7(-2) + 3$$Now use the order of operations to simplify. For example, $3(-2)^4 = 3\times(-2)^4 = 3\times16 = {48}$.
A: It appears your problem is with order of operations.
Let's look at an easier function:
$$g(x) = 6x^4$$
What is $g(-2)$?
$$g(-2) = 6(-2)^4$$
Remember--you evaluate exponents before multiplication:
$$g(-2) = 6(16)$$
$$g(-2) = 96$$
If the positive/negative thing is still hard, just turn the exponent into multiplication:
$$g(-2) = 6[(-2)(-2)(-2)(-2)]$$
$$g(-2) = 6[(-2)(-2)(4)]$$
$$g(-2) = 6[(-2)(-8)]$$
$$g(-2) = 6(16)$$
$$g(-2) = 96$$
EDIT:
From comments, it appears the error wasn't with raising the negative to an even power, but rather with the second term.  The answer has been dealt with in other responses, but I'll include it here for archive purposes:
$$f(x)=3x^4−6x^3+4x^2−7x+3$$
$$f(-2)=3(-2)^4−6(-2)^3+4(-2)^2−7(-2)+3$$
$$f(-2)=3(16)−6(-8)+4(4)−7(-2)+3$$
(Note the minus signs in front of the six and seven.  I now multiply out those negatives, which makes them positive.)
$$f(-2)=3(16)+6(8)+4(4)+7(2)+3$$
$$f(-2)=48+48+16+14+3$$
$$f(-2)=129$$
A: $$f(-2)=3\cdot(-2)^4-6\cdot(-2)^3+4\cdot(-2)^2-7\cdot(-2)+3=48+48+16+14+3=129$$
A: $$f(x)=3x^4−6x^3+4x^2−7x+3=(x+2)(3x^3-12x^2+28x-63)+129$$
$$\implies f(-2)=0(3x^3-12x^2+28x-63)+129=129$$
A: Horner's method?
$$3 + x \cdot ( -7 + x \cdot (4 + x \cdot (-6 + 3\cdot x)))=$$
$$=3 + (-2 )\cdot ( -7 + (-2) \cdot (4 + (-2) \cdot (-12)))=$$
$$=3 + (-2) \cdot ( -7 + (-2) \cdot (4 + 24))=$$
$$=3 + (-2) \cdot ( -7 + (-2) \cdot 28)=$$
$$=3 + (-2) \cdot ( -7 - 56)=$$
$$=3 + (-2) \cdot (-63)=$$
$$=129$$
