Question

Without actual division, find the remainder when 2x 3 -x2 -3x +5 is divided by
2x+1​

Answer 1

Answer:

6

Step-by-step explanation:

2x³ - x² - 3x + 5

Let us consider (2x+1) is the factor

∴ 2x + 1 = 0

2x = -1

x = $\frac{-1}{2}$

substituting;

f($\frac{-1}{2}$) = 2 x ($\frac{-1}{2}$)³ - ($\frac{-1}{2}$)² - 3 x $\frac{-1}{2}$ + 5

2 x  $\frac{-1}{8}$ - $\frac{1}{4}$ + $\frac{3}{2}$ + 5

$\frac{-1}{4}$ -  $\frac{1}{4}$ + $\frac{3}{2}$ + 5

$\frac{-1-1+6+20}{4}$ = $\frac{-2+26}{4}$ = $\frac{24}{4}$ = 6

∴ When 2x³ - x² - 3x + 5 is divided by 2x+1, the remainder is 6

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