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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.
WORKSHEET 6.5 PART 1 – Long Division of Polynomials Name: _____ Hour: _____ Date: _____ DIRECTIONS: Divide the polynomials using Long Division. 1) (x2 – 6x + 4) ÷ (x + 1) 2) (x3 + 5x2 – 4) ÷ (x + 4) 3) (10x3 + 27x2 + 14x + 5) ÷ (x2 + 2x) 4) (2x4 + 3x – 1) ÷ (x2 + 2x + 1)
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.
Synthetic Division is a method for dividing polynomials that is quicker and more efficient: Examples: e. Divide f(x) = x3 + 5x2 – 7x + 2 by x – 2 f. Determine if (x + 3) is a factor of (x) = 2x3 + x2 – 8x + 21 by using synthetic division. If so, find the other factors. Remainder Theorem: If a polynomial f(x) is divided by x – k, then ...
1. p2 − 5 p − 5 +. p − 5. 4. x2 − 6 x − 2 +. x − 7. 8. k2 − 4 k + 4 + −1 + k. 3.
Dividing Polynomials Using Long Division. Model Problems: 2 x. 3 8 x. 2 9 x 2. Example 1: Divide using long division. 2 2 x. 3 8 x 2 9 x 2. – 2 is called the divisor and 2 x. 3 8 x 2 9 x 2 is called the dividend.
Provides worked examples of how to do long division of polynomials. Illustrates two styles of formatting the long division. Explains how to handle non-zero remainders.
