Let's analyze the polynomial [tex]\( -7 - 17x + 12x^2 \)[/tex].
1. Identify the Polynomial:
The polynomial in question is:
[tex]\[
-7 - 17x + 12x^2
\][/tex]
2. Structure and Coefficients:
This is a quadratic polynomial of the form [tex]\( ax^2 + bx + c \)[/tex], where:
[tex]\[
a = 12, \quad b = -17, \quad c = -7
\][/tex]
3. Evaluate the Polynomial at x = 0:
Substituting [tex]\( x = 0 \)[/tex] into the polynomial, we get:
[tex]\[
-7 - 17(0) + 12(0^2) = -7 - 0 + 0 = -7
\][/tex]
Therefore, the polynomial evaluates to [tex]\(-7\)[/tex] when [tex]\( x = 0 \)[/tex].
4. Representation of the Polynomial:
To generalize, we can express the polynomial as a function:
[tex]\[
f(x) = -7 - 17x + 12x^2
\][/tex]
Thus:
[tex]\[
f(x) = -7 - 17x + 12x^2
\][/tex]
When evaluated at [tex]\( x = 0 \)[/tex], the result is:
[tex]\[
f(0) = -7
\][/tex]
So, the polynomial is [tex]\( f(x) = -7 - 17x + 12x^2 \)[/tex] and it evaluates to [tex]\(-7\)[/tex] when [tex]\( x = 0 \)[/tex].
