A polynomial 4x⁴+2x³-2x²+x-1 is dividend by another polynomial. g(x) ,the quotient and remainder were4x²-6x+22and (-61x)+65 find g(x
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Step-by-step explanation:
By division algorithm:
Dividend, f(x) = Divisor g(x) × quotient q(x)+ remainder r(x)
f(x) - r(x) = g(x) × q(x)
f(x) + {- r(x)} = g(x) × q(x)
If we add - r(x) to f(x) then the resulting polynomial is divisible by g(x). Now we find the remainder when f(x) is divided by g(x).
x² +2x - 3)4x⁴ + 2x³ - 2x² + x -1(4x²-6x+22
4x⁴ + 8x³- 12x²
(-) (-) (+)
-----------------------------
-6x³ +10x²+ x-1
-6x³ -12x²+18x
(+) (+) (-)
-------------------------------
22x² -17x -1
22x² + 44x -66
(-) (-) (+)
------------------------------
-61x +65
r(x) = -61x +65
Hence, we should add -r(x) = 61x - 65 to f(x) so that the resulting polynomial is divisible by g(x).
HOPE THIS WILL HELP YOU.
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