Chapter 8.1, Problem 32PPS

To determine

To write: The polynomial $\frac{1}{2}x-3x^4+7$ in standard form and identify the leading coefficient.

Answer to Problem 32PPS

The standard form of the polynomial is $-3x^4+\frac{1}{2}x+7$

The leading coefficient is $-3$

Explanation of Solution

Given:

  $\frac{1}{2}x-3x^4+7$

Calculation:

The given polynomial is $\frac{1}{2}x-3x^4+7$

A polynomial is in standard form if the exponent is arranged from largest to lowest i.e. in descending order.

So, arrange the exponent in descending order to write the polynomial in standard form.

  $-3x^4+\frac{1}{2}x+7$

Now, the coefficient of the variable with largest exponent is called leading coefficient.

Here, the coefficient of the variable with largest exponent is $-3$

Therefore, the leading coefficient is $-3$