Unit: 1.2.2 : Synthetic Division

1. (a) What is the degree of quotient when the degree of polynomial is 'n' in [br]synthetic division?[br]Solution:[br]The degree of quotient is n-1.[br][br]1. (b) What should be the expression of division in synthetic division?[br]Solution:[br]In synthetic division the divisor must be linear and dividend must be in standard form.[br][br]2. Use synthetic division and divide in each of the following:[br](a) [math] x^3 + 8 [/math] by [math] x-2 [/math][br]Solution:[br]Let [math] f(x) = x^3 + 8 [/math] [br]Zero of [math] x-2 [/math] is 2.[br]Using synthetic division, we get,[br][img]data:image/png;base64,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[/img][br]Here, quotient [math] (Q ) = x^2 + 2x + 4 [/math][br]Remainder [math] (R) = 8 [/math] [br][br]2. (b) [math] 2x^4+7x^3+x-12 [/math] by [math] (x+3) [/math][br]Solution:[br]Let, [math] f(x) = 2x^4+7x^3+0.x^2+x-12 [/math][br]Zero of [math] x+3 [/math] is [math] - 3 [/math][br]Now, using synthetic division, we get,[br][img]data:image/png;base64,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[/img][br]Here, quotient [math] = 2x^3+x^2-3x+10 [/math][br]Remainder [math] = - 42 [/math] [br][br]2. (c) [math] 4x^3-3x^2+x+9 [/math] by [math] x-2 [/math][br]Solution:[br]Let, [math] f(x) = 4x^3-3x^2+x+9 [/math][br]Zero of polynomial [math] x- 2 [/math] is 2.[br]Now, using synthetic division, we get,[br][img]data:image/png;base64,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[/img][br][math] \therefore [/math] Quotient [math] = 4x^2 + 5x + 11 [/math][br]Remainder [math] = 31 [/math][br][br]2. (d) [math] 2x^3+7x^2-8 [/math] by [math] (x+3) [/math][br]Solution:[br]Let, [math] f(x) = 2x^3+7x^2 + 0.x -8 [/math][br]Zero of [math] x+3 [/math] is -3.[br]Now, using synthetic division, we get,[br][img]data:image/png;base64,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[/img][br]Here, Quotient [math] = 2 x^2+x - 3 [/math][br]Remainder [math] = 1 [/math][br][br]2. (e) [math] 8x^3+4x^2+6x-7 [/math] by [math] 2x-1 [/math] [br]Solution:[br]Let, [math] f(x) = 8x^3+4x^2+6x-7 [/math][br]Zero of polynomial [math] 2x - 1 [/math] is [math] \frac{1}{2} [/math][br]Now, using synthetic division, we get,[br][img]data:image/png;base64,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[/img][br]Here,[br] [math] \begin{align} \text{Quotient} & = \frac{1}{2} (8x^2+8x+10 )\\ & = \frac{1}{2} \times 2 (4x^2 +4x + 5 ) \\ & = 4x^2+4x+5 \end{align} [/math] [br]Remainder [math] = -2 [/math]

Information: Unit: 1.2.2 : Synthetic Division