Question

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

Answer 1

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,

\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.