What We Have Discussed

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

2. A quadratic polynomial in x with real coefficients is of the form ax2 + bx + c , where a, b, c are real numbers with a ≠ .

3. The zeroes of a polynomial p(x) are the -coordinates of the points where the graph of y = p(x) intersects the -axis.

4. A quadratic polynomial can have at most zeroes and a cubic polynomial can have at most zeroes.

5. If α and β are the zeroes of the quadratic polynomial ax2 + bx + c, a ≠ 0 , then

α + β = -/a , αβ = /a.

6. If α , β , γ are the zeroes of the cubic polynomial ax3 + bx2 + cx + d, a ≠ 0, then

α + β + γ = (-b)/a

αβ + βγ + γα = /d

and αβγ = (-d)/

7. The division algorithm states that given any polynomial p(x) and any non-zero polynomial g(x), there exist polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x),

where either r(x) = 0 or degree r(x) < degree g(x) if r(x) ≠= 0.