Question

What is the coefficient of \[{x^2}\] in \[3{x^3} + 2{x^2} - x + 1\] ?

Answer 1

Hint: An equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=". A polynomial is an expression which is composed of variables, constants and exponents that involves only the operations of addition, subtraction, multiplication but never division by a variable.

Complete step by step answer:
Let us discuss what the polynomial is and its terms used in it. Thus, for a given polynomial in the form as below,
\[a{x^2} + bx + c = 0\]
Here, Highest degree =\[2\], Leading coefficient = $a$ and Constant = $c$. Also, \[2\] and \[1\] are degrees, $a$ and $b$ are coefficients and $c$ is constant. Now, from the above discussion, we can solve the given polynomial.So, the given polynomial is as below,
\[3{x^3} + 2{x^2} - x + 1\]
\[\Rightarrow 3{x^3} + 2{x^2} + ( - 1)x + 1\]

Here, the coefficients are\[3\],\[2\] and \[( - 1)\]. And, the highest degree is \[3\], leading coefficient is \[3\] and constant is \[1\]. So, the coefficient of the term\[{x^3}\] is \[3\], the coefficient of the term \[{x^2}\] is \[2\] and the coefficient of the term \[x\] is \[( - 1)\]. Thus, the coefficient of the term \[{x^2}\] is \[2\]. Also, if given a polynomial in a form as below,
\[\sqrt a x + 1\]
And in this we need to find the coefficient of\[{x^2}\].
This can be solved as below,
\[\sqrt a x + 1 \\
\Rightarrow 0 + \sqrt a x + 1 \\
\Rightarrow 0\,{x^2} + \sqrt a x + 1 \]
Here, zero is multiplied with \[{x^2}\].

So, the coefficient of \[{x^2}\]= 0.

Note:The highest power of the variable that occurs in the polynomial is called the degree of a polynomial. A coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number. In short, Coefficient of polynomials is the number multiplied to the variable.