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- Monomials: Algebraic expression with one term is known as Monomial.
- Binomial: Algebraic expression with two terms is called Binomial.
- Trinomial: Algebraic expression with three terms is known as Trinomial.
- Polynomials: All above mentioned algebraic expressions are called Polynomials.
- Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.
- A quadratic polynomial in x with real coefficient is of the form ax² + bx + c,where a, b, c are real numbers with a)‡0.
- 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 i.e. x = a is a zero of polynomial p(x) if p(a) = 0.
- A polynomial can have at most the same number of zeros as the degree of polynomial.
- For quadratic polynomial ax² + bx + c(a‡0) Sum of zeroes = -b/a
Product of zeroes =c/a - In a cubic polynomial ax³ + bx² + cx+d, if a(alpha), ß(bita), y(gama) are the zeroes of the polynomial,
then
a+B+ y = -b/a
aß+By+yα = c/a
a. B.y = d/a - The division algorithm states that given any polynomial p(x) and polynomial g(x), there are polynomials q(x) and r(x) such that :
p(x) = g(x).q (x) + r(x), g(x)‡0
where r(x) = 0 or degree of r(x) < degree of g(x).
Or
Dividend=Divisor x Quotient + Remainder
If r(x) = a zero polynomial, then p(x) is said to be completely divisible by g(x), i.e., g(x) is a factor of p(x).