Chapter 3: Polynomials
Now we are going to talk more about the calculation of the monomials and polynomials. In previous time, we have discussed the commonly see ways of calculating the monimials and polynomials. They are called the Properties of Exponents. It states that for all real numbers a and b, a ¹ 0, b ¹ 0, and for all integers m and n, am x an= am+n am / an = am-n (a M)n = amn ambm = (ab)m. Most time we have monomials and polynomials with positive exponents. But what about negative exponents? This is where we use the Definition of Negative Exponents. It states that for each real number a, a¹ 0, and for each integer n, a-n=1/an.
As we have seen in previous discussions that monomials and polynomials are complicated. So simplifying them before trying to solve is very important. It will improve both your speed and accuracy. Here are some basic ways to simplify the monomials and polynomials:
For all real numbers a, b, and c, b ¹ 0, cd ¹ 0, ac/bc = a/b
Definition of Multiplication of Fractions: For all real numbers a, b, c, and d, b ¹ 0, d ¹ 0,
a/b x c/d = ac/bd
Definition of Division of Fractions: For all real numbers a, b, c, and d, b ¹ 0, c ¹ 0, d ¹ 0,
a/b ¸ c/d = ad/bc
Definition of Addition of Fractions with Like Denominators: For all real numbers a, b, and c, c ¹ 0,
a/c + b/c = (a+b)/c
Definition of Inverse Variation: Two quantities x and y vary inversely if and only if there is a constant k, k ¹ 0,
such that y = k/x or xy = k
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