Summary

In this chapter, you have studied the following points:

(1) A polynomial of one term is called a .

(2) A polynomial of two terms is called a .

(3) A polynomial of three terms is called a .

(4) A polynomial of degree one is called a polynomial.

(5) A polynomial of degree two is called a polynomial.

(6) A polynomial of degree three is called a polynomial.

(7) A real number ‘a’ is a zero of a polynomial p(x) if p(a) = 0. In this case, a is also called a root of the equation p(x) = 0.

(8) Every linear polynomial in one variable has a unique zero, a non-zero constant polynomial has no zero, and every real number is a zero of the polynomial.

(9) Factor Theorem: x – a is a factor of the polynomial p(x), if p(a) = 0. Also, if x – a is a factor of p(x), then p(a) = 0.

(10) x+y+z2 = x2+ y2 + z2+ 2xy2x2y2 + 2yz2z2y2 + 2zx2x2z2

(11) x+y3 = x3 + y3+ 3xy3x2y(x + y)

(12) x−y3 = x3 - y3- 3xy(x - y)

(13) x3 + y3 + z3 – 3xyz = (x + y + z) (x2+y2+z2– xy – yz – zx)