Question

p(x)=5x^⁴+2x^3+x^2+4 divided byg(x) x-2 by remainder theorem and long division​

Answer 1

Long division

• p (x) = 5x⁴ + 2x³ + x² + 4
• q (x) = x - 2

x - 2 ) 5x⁴+2x³+x²+4 ( 5x³+ 12x² + 25x + 50

5x⁴ - 10x³

______________

12x³ + x²

12x³ - 24²

_________

25x² + 4

25x² - 50x

_________

50x + 4

50x - 100

_______

104

Answer:

• quotient = 5x³ + 12x² + 25x + 50
• remainder = 104

Remainder theorem

• p (x) = 5x⁴ + 2x³ + x² + 4
• q (x) = x - 2

Now p (2) = 5 (2)⁴ + 2(2)³ + 2² + 4

= 5 (16) + 2 (8) + 4 + 4

= 80 + 16 + 8

= 104

So the required remainder is 104.