Question

find the remainder when p(x) is divided by g(x)

p(x)=x^4 -3x^2+2x+1 ; g(x)=(1-3x)​

Answer 1

(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.

Answer 2

Answer:

The remainder is -29.

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