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Synthetic Division

Synthetic Division. Find the remainder of f(x) when divided by x-a. Ex Find the remainder of x 4 +2x 3 - 6x 2 +7x-13 when divided by x-2. Method 1 Using long division. Method 2 Using Synthetic Division. How synthetic division works:. | 1 2 -6 7 -13. 2x1. add. 2. 8. 4. 22.

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Synthetic Division

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  1. Synthetic Division Find the remainder of f(x) when divided by x-a. Ex Find the remainder of x4 +2x3 - 6x2+7x-13 when divided by x-2. Method 1 Using long division Method 2 Using Synthetic Division

  2. How synthetic division works: • | 1 2 -6 7 -13 2x1 add 2 8 4 22 _________________________________ 1 4 2 11 9 The quotient is x3+4x2+2x+11. The remainder is 9.

  3. Exercise • Find the remainder when 4x3 +2x-5 • is divided by • x – 3 • x + 5 Finish both parts before you go to the next slide.

  4. Solution Remember that coefficient of x2 = 0. (a) 3 | 4 0 2 -5 12 36 114 _____________________________ 4 12 38 109 Remainder = 28 Write x+5 as x-(-5) (b) -5| 4 0 2 -5 -510 -20 100 ____________________________ -515 4 -20 102 Remainder = -515

  5. Variation From previous example, 4x3+2x-5 when divided by x-3 leaves a quotient 4x2+12x+38 and the remainder is 109. Exercise Find the quotient and the remainder when 4x3+2x-5 is divided by 2x-6.

  6. Solution Since 4x3+2x-5 when divided by x-3 leaves a quotient 4x2+12x+38 and a remainder 109, we can write 4x3+2x-5=(x-3)(4x2+12x+38)+109. To find the quotient and the remainder when 4x3+2x-5 is divided by 2x-6. 4x3+2x-5=(x - 3)(4x2 + 12x+38)+109 =(2x-6)(2x2 + 6x+19)+109 Thus, the quotient is 2x2+6x+19 and the remainder is 109.

  7. Last exercise Find the quotient and remainder when f(x)=4x3+2x2-3x+1 is divided by 2x-1. • Hint: • Write 2x-1 = 2(x-1/2) • Apply synthetic division using x-1/2 • Deduce the quotient and remainder when • f(x) is divided by 2x-1. We shall check the answer in class.

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