Question

what are coefficients?

in easy language so that I can understand. I am really weak in maths. ​

Answer 1

Answer:

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as {\displaystyle a}a, {\displaystyle b}b and {\displaystyle c}c).[1][2][3] In the latter case, the variables appearing in the coefficients are often called parameters, and must be clearly distinguished from the other variables.

For example, in

{\displaystyle 7x^{2}-3xy+1.5+y,}{\displaystyle 7x^{2}-3xy+1.5+y,}

the first two terms have the coefficients 7 and −3, respectively. The third term 1.5 is a constant coefficient. The final term does not have any explicitly-written coefficient factor that would not change the term; the coefficient is thus taken to be 1 (since variables without number have a coefficient of 1[2]).

In many scenarios, coefficients are numbers (as is the case for each term of the above example), although they could be parameters of the problem—or any expression in these parameters. In such a case, one must clearly distinguish between symbols representing variables and symbols representing parameters. Following René Descartes, the variables are often denoted by x, y, ..., and the parameters by a, b, c, ..., but this is not always the case. For example, if y is considered a parameter in the above expression, then the coefficient of x would be −3y, and the constant coefficient (always with respect to x) would be 1.5 + y.

When one writes

{\displaystyle ax^{2}+bx+c,}{\displaystyle ax^{2}+bx+c,}

it is generally assumed that x is the only variable, and that a, b and c are parameters; thus the constant coefficient is c in this case.

Similarly, any polynomial in one variable x can be written as

{\displaystyle a_{k}x^{k}+\dotsb +a_{1}x^{1}+a_{0}}a_{k}x^{k}+\dotsb +a_{1}x^{1}+a_{0}

for some positive integer {\displaystyle k}k, where {\displaystyle a_{k},\dotsc ,a_{1},a_{0}}a_{k},\dotsc ,a_{1},a_{0} are coefficients; to allow this kind of expression in all cases, one must allow introducing terms with 0 as coefficient. For the largest {\displaystyle i}i with {\displaystyle a_{i}\neq 0}a_{i}\neq 0 (if any), {\displaystyle a_{i}}a_{i} is called the leading coefficient of the polynomial. For example, the leading coefficient of the polynomial

{\displaystyle \,4x^{5}+x^{3}+2x^{2}}\,4x^{5}+x^{3}+2x^{2}

is 4.

Some specific coefficients that occur frequently in mathematics have dedicated names. For example, the binomial coefficients occur in the expanded form of {\displaystyle (x+y)^{n}}(x+y)^{n}, and are tabulated in Pascal's triangle.

Hope it's helpful to you

Thankyou

Answer 2

$\huge\mathfrak{Answer♥♥♥}$

A number on its own is called a Constant. A Coefficient is a number used to multiply a variable (4x means 4 times x, so 4 is a coefficient) Variables on their own (without a number next to them) actually have a coefficient of 1 (x is really 1x)