The polynomial has one term, so its degree is the sum of the exponents of the variables:

\(\displaystyle 12+14 + 16+18 =60\)

The degree of a polynomial in more than one variable is the greatest degree of any of the terms; the degree of a term is the sum of the exponents. The degrees of the terms in the given polynomial are:

\(\displaystyle 50 + 30 = 80\)

\(\displaystyle 70 + 25= 95\)

\(\displaystyle 45+45 = 90\)

\(\displaystyle 30 + 70 = 100\)

The degree of the polynomial is the greatest of these degrees, 100.

The degree of a polynomial in one variable is the greatest exponent of any of the powers of the variable. The terms have as their exponents, in order, 44, 20, 10, and 100; the greatest of these is 100, which is the degree.

The degree of a polynomial in one variable is the greatest exponent of any of the powers of the variable. The terms have as their exponents, in order, 10, 20, 30, and 40; 40 is the greatest of them and is the degree of the polynomial.

The degree of a polynomial is the highest degree of any term; the degree of a term is the exponent of its variable or the sum of the exponents of its variables, with unwritten exponents being equal to 1. For each term in a polynomial, write the exponent or add the exponents; the greatest number is its degree. We do this with all four choices:

\(\displaystyle \underline{6x^{3}y^{2} + 4 xy^{3} - 100}\):

\(\displaystyle 6x^{3}y^{2}: 3 + 2 = 5\)

\(\displaystyle 4 xy^{3}: 1 + 3 = 4\)

\(\displaystyle 100:\) A constant term has degree 0.

The degree of this polynomial is 5.

\(\displaystyle \underline{7xy^{4} - 4x^{2}+ y^{3}}\)

\(\displaystyle 7xy^{4} : 1 + 4 = 5\)

\(\displaystyle 4x^{2} : 2\)

\(\displaystyle y^{3}: 3\)

The degree of this polynomial is 5.

\(\displaystyle \underline{8x ^{4}y - 4 y^{2} + 9x^{3}y}\)

\(\displaystyle 8x ^{4}y: 4 + 1= 5\)

\(\displaystyle 4 y^{2} : 2\)

\(\displaystyle 9x^{3}y: 3 + 1= 4\)

The degree of this polynomial is 5.

\(\displaystyle \underline{-5 x^{2}y^{2}+ 7x^{3}y^{2}+ 8x}\)

\(\displaystyle -5 x^{2}y^{2} : 2 + 2 = 4\)

\(\displaystyle 7x^{3}y^{2} : 3 + 2 = 5\)

\(\displaystyle 8x: 1\)

The degree of this polynomial is 5.

All four polynomials have the same degree.

The degree of a monomial term is the sum of the exponents of its variables, with the default being 1.

For each monomial, this sum - and the degree - is as follows:

\(\displaystyle 444x^{999}yz\): \(\displaystyle 999 + 1 + 1 = 1,001\)

\(\displaystyle 333x^{999}y^{999}z^{999}\): \(\displaystyle 999+999+999 = 2,997\)

\(\displaystyle 999x^{4}y^{5}z^{6}\): \(\displaystyle 4+5+6 = 15\) (note - 999 is the coefficient)

\(\displaystyle 100x^{333}y^{333}z^{333}\): \(\displaystyle 333+333+333 = 999\)

\(\displaystyle 100x^{333}y^{333}z^{333}\) is the correct choice.

The degree of the polynomial is the largest degree of any one of it's individual terms.

\(\displaystyle \small - x^{2}+3x - 2x^{5} - x^{3} +4\)

The degree of \(\displaystyle \small -x^2\) is \(\displaystyle \small 2\)

The degree of  \(\displaystyle \small 3x\) is \(\displaystyle \small 1\)

The degree of \(\displaystyle \small -2x^5\) is \(\displaystyle \small 5\)

The degree of \(\displaystyle \small -x^3\) is \(\displaystyle \small 3\)

The degree of  \(\displaystyle \small 4\) is \(\displaystyle \small 0\)

\(\displaystyle \small 5\) is the largest degree of any one of the terms of the polynomial, and so the degree of the polynomial is \(\displaystyle \small 5\).

We can add together each of the terms of the polynomial which have the same degree for our variable. \(\displaystyle (3x^{3}) + (x^{2}) + (5x+3x) + (12+8) = 3x^{3}+x^{2}+8x+20\)

Step 1: Distribute the negative to the second polynomial:

\(\displaystyle (x^4+7x^2-5x+4)-(-4x^4+5x^3-x^2+3)\)

\(\displaystyle x^4+7x^2-5x+4+4x^2-5x^3+x^2-3\)

Step 2: Combine like terms:

\(\displaystyle x^4+4x^4-5x^3+7x^2+x^2-5x+4-3\)

\(\displaystyle 5x^4-5x^3+8x^2-5x+1\)

\(\displaystyle (FG)(x) = F(x)G(x)\) so we multiply the two function to get the answer.  We use \(\displaystyle x^{m}x^{n} = x^{m+n}\)