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Objective: To divide polynomials using long and synthetic division, and to use the remainder and factor theorems. Perform long division, as you do with numbers! Remember, division is repeated subtraction, so each time you have a new term, you must ___________ it from the previous term. Work from left to right, starting with the highest degree term. Just as with numbers, there may be a remainder left. The divisor may not go into the dividend evenly. (x2 + 14x + 45) ÷ (x + 9) Write the polynomial in ___________ ________. If any power is missing, use a _______ to hold the place of that term. Divide as before. 24 33482 1 a simpler process (than long division) for dividing a polynomial by a binomial uses ___________ and part of the divisor Use Synthetic Division: 1. 2. 3. 4. 5. 6. 7. Write polynomial in ___________ order of the degrees. List the ___________. (If one power is missing, put a zero to hold that place.) Write the constant _____ of the divisor x - c to the left. Bring down the ___________ coefficient. ___________ the first coefficient by c, write the product under the 2nd coefficient and add. Multiply this sum by c, write it under the next coefficient and add. ___________ until all coefficients have been used. The numbers on the bottom row are the coefficients of the polynomial ___________. The first power on the variable will be one _________ than the highest power in the original polynomial. If the polynomial f(x) is divided by x – c , then the remainder is the ___________ f(c). f(c). x3 – 7x – 6 by x + 2. Given f(x) = 3x3 + 4x2 – 5x + 3, use the remainder theorem to find f(-4). f(x) = (x – c)q(x) + r 2 LONG DIVISION If a binomial divides into a polynomial with no remainder, the binomial is a ___________ of the polynomial. For the polynomial f(x), if f(c) = 0, 0, then x – c is a factor of f(x) Remember . . . If something is a factor, then it divides the term evenly (with 0 remainder). Solve the equation 15x3 + 14x2 – 3x – 2 = 0, given that -1 is a zero of f(x) = 15x3 + 14x2 – 3x – 2. 3