what must be subtracted from 5x^4 + 4x^3 + 3x^2 + 2x + 1 so that the result is divisible by 2x - 1
Answers
Given:
Dividend = 5x⁴ + 4x³ + 3x² + 2x + 1
Divisor = 2x - 1
To find:
What must be subtracted from 5x⁴ + 4x³ + 3x² + 2x + 1 so that the result is divisible by 2x - 1.
Solution:
2x - 1 ) 5x⁴ + 4x³ + 3x² + 2x + 1 ( 2x³ + 3x² + 3x + 2
4x⁴ - 2x³ ↓ ↓ ↓
(-) (+)
x⁴ + 6x³ + 3x²
6x³ - 3x²
(-) (+)
x⁴ + 6x² + 2x
6x² - 3x
(-) (+)
x⁴ + 5x + 1
4x - 2
(-) (+)
x⁴ + x + 3
Quotient = 2x³ + 3x² + 3x + 2
Remainder = x⁴ + x + 3
Therefore, x⁴ + x + 3 must be subtracted from 5x⁴ + 4x³ + 3x² + 2x + 1 so that the result is diisible by 2x - 1.
Result after subtraction x⁴ + x + 3 form 5x⁴ + 4x³ + 3x² + 2x + 1.
5x⁴ + 4x³ + 3x² + 2x + 1
x⁴ + x + 3
(-) (-) (-)
4x⁴ + 4x³ + 3x² + x - 2