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given that x+2 is a factor of 2x^3+6x^2+dx-5, find the remainder when the expression is divided by 2x-1

Answer :

MHANIFAGO

Answer:

  • -2.5

Step-by-step explanation:

Given:

  • x + 2 is a factor of 2x³ + 6x² + dx - 5

Work out the value of d:

(2x³ + 6x² + dx - 5) ÷ (x + 2) =  2x² + 2x - 2.5

2x³ + 4x²

         2x² + dx

         2x² + 4x

                    (d-4)x - 5

  • -5/2 = -2.5
  • d - 4 = -2.5 ⇒ d = 1.5

The expression is:

  • 2x³ + 6x² + 1.5x - 5

Divide it by 2x - 1:

(2x³ + 6x² + 1.5x - 5) ÷ (2x - 1) = x² + 3.5x + 2.5

2x³ - x²

        7x² + 1.5x

        7x² - 3.5x

                  5x - 5

                  5x - 2.5

                         -2.5

The remainder is -2.5

         

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