Question

What is the degree of the polynomial -6x^3y² + 5x^4- 7z

Answer 1

To determine the degree of a polynomial, you need to find the highest sum of the exponents of the variables in each term.

Let's analyze each term in the polynomial \(-6x^3y^2 + 5x^4 - 7z\):

1. For the term \(-6x^3y^2\):
- The exponent of \(x\) is 3.
- The exponent of \(y\) is 2.
- The sum of the exponents is \(3 + 2 = 5\).

2. For the term \(5x^4\):
- The exponent of \(x\) is 4.
- Since there are no other variables, the sum of the exponents is \(4\).

3. For the term \(-7z\):
- The exponent of \(z\) is 1.
- Since there are no other variables, the sum of the exponents is \(1\).

Now, we compare the highest sums:
- From \(-6x^3y^2\), the degree is 5.
- From \(5x^4\), the degree is 4.
- From \(-7z\), the degree is 1.

The highest degree among these is \(5\).

Therefore, the degree of the polynomial \(-6x^3y^2 + 5x^4 - 7z\) is **5**.