Use remainder theorem to find remainder when p(x) is divided by q(x) in the following equation i.) p(x)= ______ q(x) = x-1
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(a) Q(X) =0
X +2 = 0
X = -2
P(X) = 2X³-3X²+4X-1
P(-2) = 2 × (-2)³ -3 × (-2)² + 4 × -2 -1
=> 2 × -8 - 3 × 4 -8-1
=> -16 -12-1 = -29
when P(X) divided by G(X) then reminder comes -29.
(B) X³-6X²-2X-4
Q(X) = 0
1-3X = 0
3X = 1
X = 1/3
P(X) = X³-6X²-2X-4
P(1/3) = (1/3)³ - 6 × (1/3)² - 2 × 1/3 -4
=> 1/27 - 6 × 1/9 -2/3 -4
=> 1/27 - 2/3 -2/3 -4
=> 1 - 18 - 18 - 108
=> -108 -36+1 = .-144+1 = -143.
When P(X) Divided by G(X) then reminder comes 73.
(C) 3X²+X-2
=> 3X²+3X-2X-2
=> 3X(X+1) -2(X+1)
=> (X+1) (3X-2)
=> (X+1) = 0. OR (3X-2) = 0
=> X = -1 OR X= 2/3
-1 and 2/3 are the two zeros of the polynomial 3X²+X-2.
HOPE IT WILL HELP YOU..... :-)
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