Question

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

Answer 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