In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):
f(x) = 4x³ -12x²+14x-3, g(x) = 2x-1
Answers
Given : f(x) = 4x³ - 12x² + 14x - 3, g(x) = 2x - 1
By remainder theorem, when f(x) is divided by g(x) = 2x - 1 , the remainder is equal to f(1/2) :
Now, f(x) = (x) = 4x³ - 12x² + 14x - 3
f(1/2) = 4(1/2)³ - 12 (1/2)² + 14 (1/2) - 3
f(1/2) = 4 × ⅛ - 12 × 1/4 + 14/2 - 3
f(1/2)= ½ - 3 + 7 - 3
f(1/2) = ½ - 6 + 7
f(1/2) = ½ + 1
f(1/2) = (1 + 2)/2
f(1/2) = 3/2
Hence, the remainder when f(x) is divided by g(x) is 3/2.
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Some more questions :
In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):
f(x) = 2x⁴-6x³+2x²-x+2, g(x) = x+2
brainly.in/question/15903847
In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):
f(x) = 3x⁴+2x³ x²/3 - x/9 + 2/27, g(x) = x+ 2/3
brainly.in/question/15903848
Step-by-step explanation:
no
Solution :
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Factor Theorem :
Let p(x) be a polynomial of degree
one or more than 1 and a is a real
number. Then ,
i ) x - a , will be a factor of p(x) if
p(a) = 0 conversely
ii ) If ( x - a ) is a factor of p(x) , then
p(a) = 0.
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Given
f(x) = 4x³ + 20x² + 33x + 18 ,
g(x) = 2x + 3 ,
g(x) = 0
=> 2x + 3 = 0
=> x = -3/2
Now , f( -3/2 )
= 4(-3/2)³ + 20(-3/2)² + 33(-3/2) + 18
= 4(-27/8) + 20(9/4) - 33(3/2 ) + 18
= -27/2 + 5 × 9 - 99/2 + 18
= ( -27 - 99 )/2 + 45 + 18
= - 126/2 + 63
= - 63 + 63
= 0
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