Question

remainder theorem: find the remainder when x^3+3x^2+3x+1 by 5+2x​

Answer 1

Answer:

Remainder =$-\frac{27}{8}$

Step-by-step explanation:-

Dividend = x³ + 3x² + 3x + 1

Divisor = 5 + 2x

apply remainder theorem

5 + 2x = 0

2x = -5

x = $-\frac{5}{2}.$

replace x by $\frac{-5}{2}$ , we get

p(x) x³ + 3x² + 3x + 1

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

= $\frac{-125}{8}$ +$\frac{75}{4}$ - $\frac{15}{2}$ + 1

= $\frac{-125+150-60+8}{8}$

= $-\frac{27}{8}.$

Therefore the remainder is $-\frac{27}{8}.$