Arithmetic Course/Polynomial

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Polynomial[edit]

A polynomial is a variable that has the general form

P(x) = a_n x^n + a^n-1 x^n-1 + a_1 x + a_o

Here, the a literals represent any constant numbers.

Monomial[edit]

Polynomials with highest degree as 1 are called Monomials. Monomial has the general form

P(x) = a x

Consider y as a monomial function of x.

y = 2 x
x | y
-2 | -4
-1 | -1
0 | 0
1 | 1
2 | 2


General equation of a straight line with slope m = a through y intercept (0,b)

  • P(x) = a x + b

Equation of a straight line with slope m = 1 and passing through (0,0).

y = x
x | -2 -1 0 1 2
y | -2 -1 0 1 2

Binomial[edit]

Polynomial of one variable has the general form

  • P(x) = a x^2
y = a x^2
x | -2 -1 0 1 2
y | 4 2 0 2 4
Parabola goes through point (0,0)
  • P(x) = a x^2 + c
Parabola goes through y - intercept point (0,\frac{c}{a})
  • P(x) = a x^2 - c
Parabola goes through y - intercept point (0,\frac{c}{a})
  • P(x) = a x^2 + b x
  • P(x) = a x^2 + b x + c