Summary
1. Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively. i.e, Linear polynomials: $ax+b$ quadratic polynomial: $ax^2+bx+c$ cubic polynomial : $ax^3+bx^2+cx+d$ 2. A quadratic polynomial in ${x}$ with real coefficients is of the form ${ax^2 + bx + c}$, where a, b, c are real numbers with a ≠ 0. 3. 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.Zeros of a linear polynomial $ax + b$ is ${-b/a}$ 4. In general, given a polynomial $p(x)$ of degree $n$, the graph of $y=p(x)$ intersects the x-axis at atmost $n$ points. Therefore, a polynomial p(x) of degree $n$ has at most $n$ zeroes.A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes. 5. If α and β are the zeroes of the quadratic polynomial ${ax^2 + bx + c}$, then α +β = ${-b/a}$ αβ = ${c/a}$ 6. If α, β, γ are the zeroes of the cubic polynomial $ax^3+bx^2+cx+d$, then α +β + γ = ${-b/a}$ αβ+ β γ + γ α = ${c/a}$ and αβ γ = ${-d/a}$ 7. The division algorithm states that given any polynomial ${p(x)}$ and any non-zero polynomial ${g(x)}$, there are polynomials ${q(x)}$ and ${r(x)}$ such that ${p(x)= g(x)q(x) + r(x)}$, where ${r(x) = 0 }$ or degree ${r(x)}$ < degree ${g(x)}$.