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 ax2 + bx + c, where a, b, c are the real numbers and a ≠ 0.
4. A cubic polynomial in x is of the
form ax3 + bx2 + cx + d, where a, b, c, d are the
real numbers and a ≠ 0.
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 α
and β are the zeroes of the quadratic polynomial ax2 + bx + c, then
α + β = -b/a
and
αβ = c/a.
8. If α,
β and γ are the zeroes of the quadratic polynomial ax2 + bx + c, then
α + β + γ =
-b/a, αβ + βγ + γα = c/a and
αβγ = -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).