Question

For the polynomial $4x-6x^5+3x^2$, find the coefficient of the second term when this polynomial is written in standard form.

Answer 1

Given a polynomial $4x-6x^5+3x^2$.

$\underset{–}{Step1}$

Writing the polynomial $4x-6x^5+3x^2$ in standard form.
The term $-6x^5$ has the highest power of the variable $x$. This term would be the first term in standard form of the polynomial $4x-6x^5+3x^2$.

The term $3x^2$ has the second highest power of the variable $x$. This term would be the second term in standard form of the polynomial $4x-6x^5+3x^2$.

The term $4x$ has the third highest power of the variable $x$. This term would be the third term in standard form of the polynomial $4x-6x^5+3x^2$.

The standard form of the polynomial $4x-6x^5+3x^2$:
$-6x^5+3x^2+4x$

The second term in standard form of the polynomial $4x-6x^5+3x^2$ is $3x^2$.

$\underset{–}{Step2:}$

The standard form of the polynomial $4x-6x^5+3x^2$:
$-6x^5+3x^2+4x$

Coefficient of $x^5=-6$
Coefficient of $x^2=3$
Coefficient of $x=4$

The coefficient of $x^2$, i.e., second term when the polynomial $4x-6x^5+3x^2$ is written in standard form is $3$.