Question

When multiplying polynomials for a math assignment, Pat found the product to be -4x+8r2 - 2x +5. He then had to state the leading coefficient and the degree of this
polynomial. Pat wrote down -4 for the leading coefficient and 1 for the degree. Do you agree with pat's answer? Explain your reasoning.​

Answer 1

SOLUTION

TO DETERMINE

When multiplying polynomials for a math assignment, Pat found the product to be - 4x + 8x² - 2x³ + 5 He then had to state the leading coefficient and the degree of this polynomial. Pat wrote down -4 for the leading coefficient and 1 for the degree. Do you agree with pat's answer? Explain your reasoning.

CONCEPT TO BE IMPLEMENTED

Polynomial

Polynomial is a mathematical expression consisting of variables, constants that can be combined using mathematical operations addition, subtraction, multiplication and whole number exponentiation of variables

DEGREE OF A POLYNOMIAL

Degree of a polynomial is defined as the highest power of its variable that appears with nonzero coefficient

Leading coefficient

The leading term is the term with the highest power, and its coefficient is called the leading coefficient.

EVALUATION

Here the given polynomial is

- 4x + 8x² - 2x³ + 5

Now the given polynomial can be rewritten as

$\sf{ - 2 {x}^{3} + 8 {x}^{2} - 4x + 5 }$

So the variable is x

Now the the highest power of its variable that appears with nonzero coefficient = 3

So the degree of the polynomial = 3

We know that leading term is the term with the highest power, and its coefficient is called the leading coefficient.

So the leading term = - 2x³

Leading coefficient = - 2

But Pat wrote down -4 for the leading coefficient and 1 for the degree

Hence Pat's answer was wrong

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Write the degree of the polynomial :

4z3 – 3z5 + 2z4 + z + 1

https://brainly.in/question/7735375

2. Find the degree of 2020?

https://brainly.in/question/25939171