without actual division prove that p(x)= x⁴+2x³ -2x²-2x-3 is exactly divisible by g(x)= x²+2x-3​

1 thought on “without actual division prove that p(x)= x⁴+2x³ -2x²-2x-3 is exactly divisible by g(x)= x²+2x-3​”

1. Step-by-step explanation:

   g(x) = x²+2x – 3 = 0

   x² + 3x – x +3 =0

   x(x + 3) – 1(x + 3) =0

   (x+3) (x–1) = 0

   x + 3= 0. : x –1=0

   x = –3. : x= 1

   p(x)= x⁴+2x³ –2x²–2x –3

   p(–3) = (–3)⁴ + 2(–3)³ – 2(–3)² – 2(–3) –3

   = 81 + (–54) – (18) – (–6) – 3

   = 81 –54 –18 + 6–3

   = 87 – 75

   = 12

   p(1) = x⁴+ 2x³–2x²–2x–3

   = 1⁴ +2(1)³ –2(1)²– 2(1) –3

   = 1 +2 – 2 – 2 –3

   = –4

   I Hope its helpful

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