# Can someone explain this to me? (1 Viewer)

#### RakeshCristoval

##### Member
Have my first ever econ1202 lecture and just do not understand what my lecturer is doing with the examples ( f(x) =2, f(x) = 1 + 0.5x and so on ) he is giving in the pic below. Was wondering if someone could explain what is going on here lol. Cheers

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#### Qeru

##### Well-Known Member
Have my first ever econ1202 lecture and just do not understand what my lecturer is doing with the examples ( f(x) =2, f(x) = 1 + 0.5x and so on ) he is giving in the pic below. Was wondering if someone could explain what is going on here lol. Cheers
The general form of a polynomial is: $\bg_white f(x)=c_nx^n+c_{n-1}x^{n-1}+...+c_1x+c_0$

where all the c's are constants and all the x's are variables

ANY polynomial can be represented in this form. For example if I let $\bg_white c_1=0.5$ and $\bg_white c_0=1$ and every other c=0 notice how the only terms im left with are the $\bg_white c_1$ and $\bg_white c_0$ terms (all the other terms become zero) so the polynomial becomes: $\bg_white f(x)=0.5x+1$. This is just one specific random example of a polynomial.

#### RakeshCristoval

##### Member
The general form of a polynomial is: $\bg_white f(x)=c_nx^n+c_{n-1}x^{n-1}+...+c_1x+c_0$

where all the c's are constants and all the x's are variables

ANY polynomial can be represented in this form. For example if I let $\bg_white c_1=0.5$ and $\bg_white c_0=1$ and every other c=0 notice how the only terms im left with are the $\bg_white c_1$ and $\bg_white c_0$ terms (all the other terms become zero) so the polynomial becomes: $\bg_white f(x)=0.5x+1$. This is just one specific random example of a polynomial.

I sort of get that but in the third example, why is c2=1? Where is he getting that?

#### Qeru

##### Well-Known Member
I sort of get that but in the third example, why is c2=1? Where is he getting that?
$\bg_white c_0$ corresponds to the constant term, $\bg_white c_1$ corresponds to to the term in x. $\bg_white c_2$ corresponds to the term in $\bg_white x^2$ c_3 corresponds to the term in $\bg_white x^3$ and so on. So by letting $\bg_white c_2=1$ your letting the coefficient of $\bg_white x^2$ equal to 1, and all the other c's are zero so they all cancel.

#### RakeshCristoval

##### Member
$\bg_white c_0$ corresponds to the constant term, $\bg_white c_1$ corresponds to to the term in x. $\bg_white c_2$ corresponds to the term in $\bg_white x^2$ c_3 corresponds to the term in $\bg_white x^3$ and so on. So by letting $\bg_white c_2=1$ your letting the coefficient of $\bg_white x^2$ equal to 1, and all the other c's are zero so they all cancel.
this makes much more sense thank you!