Answer:
Q(x) = 2x² - x + 3 , R = - 5
Step-by-step explanation:
given
2x³ + 5x² + 4 = (x + 3)Q(x) + R
Q(x) is the quotient , R the remainder and (x + 3) the divisor
When a polynomial is divided by (x + a) , the quotient is Q(x) and the remainder is R
Consider the left side
using synthetic division
- 3 | 2 5 0 4 ← 0 is the coefficient of the x- term
↓ - 6 3 - 9
------------------
2 - 1 3 - 5
Then Q(x) = 2x² - x + 3 and R = - 5
As a check
(x + 3)(2x² - x + 3) - 5
= 2x³ - x² + 3x + 6x² - 3x + 9 - 5
= 2x³ + 5x² + 4 ← the original polynomial
Then Q(x) = 2x² - x + 3 and R = - 5
