“Polynomial” comes from the word ‘Poly’ (Meaning Many) and ‘nomial’ (in this case meaning Term)-so it means many terms.
A polynomial is made up of terms that are only added, subtracted or multiplied.
A quadratic polynomial in x with real coefficients is of the form ax² + bx + c, where a, b, c are real numbers with a ≠ 0.
Degree – The highest exponent of the variable in the polynomial is called the degree of polynomial. Example: 3x3 + 4, here degree = 3.
Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomial respectively.
A polynomial can have terms which have Constants like 3, -20, etc., Variables like x and y and Exponents like 2 in y².
These can be combined using addition, subtraction and multiplication but NOT DIVISION.
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.
If α and β are the zeroes of the quadratic polynomial ax² + bx + c, then sum of zeros,α+β=−ba=−coefficientofxcoefficientofx2 product of zeros,αβ=ca=constanttermcoefficientofx2
If α, β, γ are the zeroes of the cubic polynomial ax3 + bx2 + cx + d = 0, then α+β+γ=−ba=−coefficientofx2coefficientofx3 αβ+βγ+γα=ca=coefficientofxcoefficientofx3 αβγ=−da=−constanttermcoefficientofx3
