Other Concepts chapter 2 can study by students of class 9. These definitiona and formulas of Class 9 Maths Chapter 2: Polynomial is developed and witten by our expert teachers. Maths formulas. Other Concepts is prepapred and collected from varius resources to help the students.
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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.
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 zero polynomial.
Remainder Theorem : If p(x) is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial x – a, then the remainder is p(a).
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.
The highest power of the variable in a polynomial as the degree of the polynomial
The degree of a non-zero constant polynomial is zero.
Identity I : (x + y)2 = x2 + 2xy + y2
Identity II : (x – y)2 = x2 – 2xy + y2
Identity III : x2 – y2 = (x + y) (x – y)
Identity IV : (x + a) (x + b) = x2 + (a + b)x + ab
Identity V : (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
Identity VI : (x + y)3 = x3 + y3 + 3xy (x + y)
Identity VII : (x – y)3 = x3 – y3 – 3xy(x – y)
= x3 – 3x2y + 3xy2 – y3
Identity VIII : x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – zx)
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