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A2 – Section 5.5 Date_______________ The Remainder & Factor Theorems There are ______ ways to divide polynomials; ______________________ and _______________________. Long division always works, but synthetic division only works for a ______________ whose leading coefficient is +1. Long Division 1. Rewrite the polynomial you’re dividing in _________________________. Include ______ descending powers even in they are not in the original problem. 3. 4. _____________ the term with the greatest exponent of the divisor. _____________ _____________ ________ the 2. 5. Bring the next term down. remainder divisor Ex 1 Divide. a) (8y3 – 10y2 + 5y – 9) (2y – 1) to the answer polynomial. b) (y4 + 2y2 – y + 5) (y2 – y + 1) Factor Theorem: x – h is a factor of f(x) _______________________ f(h) = 0. Remainder Theorem: If f(x) is divided by (x – h), then, the remainder equals f(h), ____________. Synthetic Division: Uses _________________ to divide 1. 2. 3. 4. Write the coefficients of the polynomial in ___________________ including all descending powers. Bring down the first coefficient. _______________ _______________ The __________ number under the box is the remainder. The other numbers stand for the coefficients of the answer polynomial whose greatest exponent, degree, is _______ less than the original. Ex 2 Divide (x3 – x2 – 2x + 8) by (x – 1). Ex 3 Factor f(x) = 3x3 + 13x2 + 2x – 8 given that f(-4) = 0. Ex 4 One zero of the f(x) = 2x3 – 9x2 – 32x – 21 is x = 7. Find the other zeros.