What is a monic polynomial? Are all polynomials monic?

Question

campbell_st · Answer

monic means the leading coefficient of the polynomial is 1... 

e.g 

$$y = x^2 + 3x$$

the leading term is x^2   and the coefficient of x^2 is 1

osanseviero · Answer

so y= 2x2 + 2 is not monic?

campbell_st · Answer

thats correct... the coefficient of the leading term is 2

osanseviero · Answer

I read something about using -b/2 as x to change the function to monic...is it still the same?

campbell_st · Answer

well if you have a quadratic 

$$ax^2 + bx + c$$

to change it to monic, divide every term by a

so 

$$x^2 + \frac{b}{a}x + \frac{c}{a} $$

hope that makes sense

osanseviero · Answer

oh...well...but is it still the same? (I think yes), so all polynomials can be expressed as monic

campbell_st · Answer

thats correct... it may look familiar if you have do sum and product of the roots of a polynomial

osanseviero · Answer

Thanks!

osanseviero · Answer

I've done it