What number should be subtracted from
2x³-5x²+5x so that the resulting polynomial has 2x-3 as a factor
Answers
Answer:
3
Step-by-step explanation:
Let a would be subtracted.
As 2x - 3 is a factor, using factor theorem,
for x = 3/2 :
⇒ 2x³ - 5x² + 5x - a = 0
⇒ 2(3/2)³ - 5(3/2)² + 5(3/2) = a
⇒ 2(27/8) - 5(9/4) + 15/2 = a
⇒ (27/4) - (45/4) + (15/2) = a
⇒ ( 27 - 45 + 30 )/4= a
⇒ 12 / 4 = a
⇒ 3 = a
Hence 3 should be subtracted
Answer:
_x²_- x_+ 1_____
2x - 3 Г2x³ - 5x² + 5x
2x³ - 3x² ∫
(-) (+) ∫
----------- ∫
-2x² + 5x
-2x² + 3x
(+) (-)
---------------
2x
2x - 3
(-) (+)
----------
3
----------
3 is the reminder so to exactly divide the above equation by 2x - 3
3 should be added to the above equation
Step-by-step explanation: