**Important Concepts and Formulas**

1. Polynomials of degrees 1, 2 and 3 are
called linear, quadratic and cubic polynomials, respectively.

2. A linear polynomial in x is of the
form

*ax + b*.
3. A quadratic polynomial in x is of the
form

*ax*, where a, b, c are the real numbers and a ≠ 0.^{2}+ bx + c
4. A cubic polynomial in x is of the
form

*ax*, where a, b, c, d are the real numbers and a ≠ 0.^{3}+ bx^{2}+ cx + d
5. The zeroes of a polynomial p(x) are
precisely the x-coordinates of the points, where the graph of y = p(x)
intersects the x-axis.

6. A linear polynomial can have at most
1 zero, a quadratic polynomial can have at most 2 zeroes and a cubic polynomial
can have at most 3 zeroes.

7. If Î±
and Î² are the zeroes of the quadratic polynomial

*ax*, then^{2}+ bx + c
Î± + Î² = -b/a
and
Î±Î² = c/a.

8. If Î±,
Î² and Î³ are the zeroes of the quadratic polynomial

*ax*, then^{2}+ bx + c
Î± + Î² + Î³ =
-b/a, Î±Î² + Î²Î³ + Î³Î± = c/a and
Î±Î²Î³ = -d/a.

9. The division algorithm states that for any
polynomial p(x) and any non-zero polynomial g(x), there exists polynomials q(x)
and r(x) such that

p(x) = g(x)
q(x) + r(x), where r(x) = 0 or degree of r(x) < degree of g(x).