check wether the polynomial f(x)=4x^3+4x^2-x-1 Is a multiple of 2x+1
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Question :-
Checking whether the given polynomial is a multiple of g(x)
Given :-
P(x) = 4x³ + 4x²-x-1
G(x) = 2x+1 =
= x = -1/2
"Remainder theorem "
Putting the value of x in polynomial :-
4x³+4x²-x-1 = 0
=> 4(-1/2)³ + 4(-1/2)² - (-1/2) -1 =0
=> 4 * -1/8 + 4/4 +1/2 -1 =0
=> -1/2 +1 +1/2 -1 =0
Hence, By Remainder theorem it proved that 2x+1 is a factor of polynomial
and poly is a multiple of 2x+1.........
Hence proved
Verified ✔️
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