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AS1.4: POLYNOMIAL LONG DIVISION . One polynomial may be divided by another of lower degree by long division (similar to arithmetic long division). Example. ( x. 3 x. 2. x + 9) ( x + 2) Write the question in long division form. Begin with the x3 term. x3 divided by x equals x2. Place x2 above the division bracket as shown.
In order to simplify certain sorts of algebraic fraction we need a process known as polynomial division. This unit describes this process. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that all this becomes second nature.
1. p2 − 5 p − 5 +. p − 5. 4. x2 − 6 x − 2 +. x − 7. 8. k2 − 4 k + 4 + −1 + k. 3.
DIRECTIONS: Divide the polynomials using Long Division. 1) ( x 2 – 6 x + 4) ÷ ( x + 1) 2) ( x 3 + 5 x 2 – 4) ÷ ( x + 4) 3) (10 x 3 + 27 x 2 + 14 x + 5) ÷ ( x 2 + 2 x ) 4) (2 x 4 + 3 x – 1) ÷ ( x 2 + 2 x + 1)
LESSON. 3-4. Practice B. Dividing Polynomials. Divide by using long division. 1. (x 2. x. (x y 6) 3) _________________________________________ 3. ( 3x 2. 20x. (x y 12) 6) _________________________________________ Divide by using synthetic division. 5. (3x 2 8x 4) y (x 2) _________________________________________
Polynomial Long Division Version 2 Name: _____ Date: _____ Score: _____ 1) 2 6 4 4 2 4 x x x x y 52 4 3 22 4 5 8 28 24 x x x x x 2) 3 1 2 xx y 4 3 6 12 2432 47 2 x x x x 3) 2 1 1 xx y 6 2 2 2 2 2 25 4 3 2 1 1 x x x x x x Direction: Divide the polynomials using “Long Method”.
Synthetic Division is a method for dividing polynomials that is quicker and more efficient than long division: Examples: d. Divide f(x) = x3 + 5x2 – 7x + 2 by x – 2. e. Determine if (x + 3) is a factor of f(x) = 2x3 + x2 – 8x + 21 by using synthetic division.
