Question

EXERCISE 2.3 find remainder x³ + 3x²+3x+1 by x = -1/2
​

Answer 1

Answer:

Using remainder theorem, remainder = 1/8

Step-by-step explanation:

$x = - \frac{1}{2} \\ p(x) = {x}^{3} + 3 {x}^{2} + 3x + 1 \\ p( - \frac{1}{2} ) = ( { \frac{ - 1}{2} }^{3} ) + 3( { \frac{ - 1}{2} }^{2} ) + 3( \frac{ - 1}{2} ) + 1 \\ = \frac{ - 1}{8} + 3 \times \frac{ 1}{4} + 3 \times \frac{ - 1}{2} + 1 \\ = \frac{ - 1}{8} + \frac{3}{4} - \frac{3}{2} + 1 \\ = \frac{ - 1 + 6 - 12 + 8}{8} \\ = \frac{14 - 13}{8} \\ = \frac{1}{8}$