What is the result of dividing 2x³ + x² - 2x + 8 by x + 2?

Solution:

If (x + 2) is a factor of 2x³ + x² - 2x + 8 then one of the zeroes of the equation is x + 2 = 0 which means:

x + 2 = 0 ⇒ x = -2

Substituting the value of x = -2 in the equation we get:

= 2(-2)³ + (-2)² - 2(-2) + 8

= 2(-8) + 4 + 4 + 8

= -16 + 16

= 0

Hence (x + 2) completely divides the above equation. Using the long division method we first multiply the divisor (x + 2) by 2x²  we get

                   2x³ + x² - 2x + 8
Subtracting 2x³ + 4x²
                  ------------------------
                     0 - 3x² - 2x + 8 → Remainder

The quotient is 2x²

In the next step we multiply the divisor (x + 2) by -3x and subtract it from the remainder

                   -3x² - 2x + 8
Subtracting -3x² - 6x
                   --------------------
                     0 + 4x + 8 → Remainder

The quotient is now 2x² - 3x

The divisor (x + 2) is now multiplied by 4 and subtracted from the last remainder

                   4x + 8
Subtracting 4x + 8
                 ------------
                    0 + 0 → Remainder

The final Quotient is 2x² - 3x + 4

Therefore on dividing 2x³ + x² - 2x + 8 by x + 2 we get

A quotient of 2x² - 3x + 4 and remainder zero

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What is the result of dividing 2x³ + x² - 2x + 8 by x + 2?

Summary:

The result of dividing 2x³ + x² - 2x + 8 by x + 2 is 2x² - 3x + 4.