<span>Polynomials can be classified two different ways - by the number of terms and by their degree.
1. Number of terms.
<span><span>A monomial has just one term. For example, 4x2 .Remember that a term contains both the variable(s) and its coefficient (the number in front of it.) So the is just one term.</span> <span>A binomial has two terms. For example: <span>5x2</span> -4x</span> <span>A trinomial has three terms. For example: <span>3y2</span>+5y-2</span> <span>Any polynomial with four or more terms is just called a polynomial. For example: <span>2y5</span><span>+ 7y3</span><span>- 5y2</span>+9y-2</span></span>
Practice classifying these polynomials by the number of terms:
2. Degree. The degree of the polynomial is found by looking at the term with the highest exponent on its variable(s).
Examples: <span><span>5x2-2x+1 The highest exponent is the 2 so this is a <span>2nd degree</span> trinomial.</span> <span>3x4+4x2The highest exponent is the 4 so this is a <span>4th degree</span> binomial.</span> <span>8x-1 While it appears there is no exponent, the x has an understood exponent of 1; therefore, this is a <span>1st degree</span> binomial.</span> <span>5 There is no variable at all. Therefore, this is a 0 degree monomial. It is 0 degree because x0=1. So technically, 5 could be written as 5x0.</span> <span>3x2y5 Since both variables are part of the same term, we must add their exponents together to determine the degree. 2+5=7 so this is a <span>7th degree</span> monomial.</span></span> Classify these polynomials by their degree.
Width would have to be a quadratic Use long division to find the other factor of the cubic polynomial P (x). P (x) factors in case it is reducible over R[x] if it weren't then P (x) mod R [x] would be a field otherwise you could use the Eisenstein Criterion.
