Pls someone give the summary of polynomials class 9 fastly pls no smapping. I will make u brainliest
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Step-by-step explanation:
An algebraic expression p(x) = a0xn + a1xn-1 + a2xn-2 + … an is a polynomial where a0, a1, ………. an are real numbers and n is non-negative integer.
A term is either a variable or a single number or it can be a combination of variable and numbers.
The degree of the polynomial is the highest power of the variable in a polynomial.
A polynomial of degree 1 is called as a linear polynomial.
A polynomial of degree 2 is called a quadratic polynomial.
A polynomial of degree 3 is called a cubic polynomial.
A polynomial of 1 term is called a monomial.
A polynomial of 2 terms is called binomial.
A polynomial of 3 terms is called a trinomial.
A real number ‘a’ is a zero of a polynomial p(x) if p(a) = 0, where a is also known as root of the equation p(x) = 0.
A linear polynomial in one variable has a unique zero, a polynomial of a non-zero constant has no zero, and each real number is a zero of the zero polynomial.
Remainder Theorem: If p(x) is any polynomial having degree greater than or equal to 1 and if it is divided by the linear polynomial x – a, then the remainder is p(a).
Factor Theorem : x – c is a factor of the polynomial p(x), if p(c) = 0. Also, if x – c is a factor of p(x), then p(c) = 0.
The degree of the zero polynomial is not defined.
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
(x + y)3 = x3 + y3 + 3xy(x + y)
(x – y)3 = x3 – y3 – 3xy(x – y)
x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)
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