Question

State the degree of the polynomial: 5x^4y – 7x^3z^3 + 27x^2.

Answer 1

The degree of the polynomial 5x^4y - 7x^3z^3 + 27x^2 is 6, based on the term with the highest sum of exponents.

Step-by-step explanation:

The degree of the polynomial 5x^4y – 7x^3z^3 + 27x^2 is determined by the highest sum of the exponents in a single term. The first term 5x^4y has a degree of 4 + 1 = 5 because the exponents of x and y are 4 and 1, respectively. The second term 7x^3z^3 has a degree of 3 + 3 = 6 because the exponents of x and z are 3. The last term, 27x^2, has a degree of 2. Therefore, the term with the highest degree is the second term with a degree of 6. This makes the entire polynomial a degree 6 polynomial.

Answer 2

The degree of the polynomial 5x^4y - 7x^3z^3 + 27x^2 is 6, as it is the highest sum of the exponents in any single term of the polynomial.

Step-by-step explanation:

The degree of the polynomial 5x^4y − 7x^3z^3 + 27x^2 is determined by looking at the exponents of each term. In a polynomial, the degree is the highest sum of the exponents of variables in any single term. For the term 5x^4y, the exponents of x and y add up to 4+1=5. For 7x^3z^3, the sum is 3+3=6. Finally, for 27x^2, the exponent is 2. Therefore, the greatest sum of exponents is 6 in the term 7x^3z^3, which means the degree of the polynomial is 6.