To divide by a monomial, divide each term of the numerator by the denominator; then write the sum of the results. We use the property of rational numbers that
a + b/c = a/c + b/c
Step 1: Divide each term of the polynomial by the monomial.
Step 2: When dividing variables, use the property x a / x b = x a - b
Division of a polynomial by a binomial is similar to long divison in arithmetic. Notice the similarity in the following division problems.
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| To check, (21) (32) = 672. | To check, (2x + 1) (3x + 2) 6x2 + 7x + 2. |
Step 1: Place the terms of the polynomial and binomial in descending order.
Insert a 0 for any missing term.
Step 2: Divide the first term of the polynomial by the first term of the binomial.
The result is the first term of the quotient.
Step 3: Multiply the first term of the quotient by their binomial and subtract the product from the first two terms of the polynomial. Bring down the next term to obtain a new polynomial.
Step 4: Divide the new polynomial by the binomial using the process described in step 2.
Step 5: Continue dividing, multiplying, and subtracting until the remainder has a lower exponent than the variable in the first term of the binomial divisor.
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