Question

WITHOUT ACTUAL DIVISION PROVE THAT X^4+2X^3-2X^2+2X-3 IS ACTAULLY DIVISIBLE BY X^2+2X-3 SPAM ANSWERS WILL BE REPORTED.

Answer 1

Answer:

the roots of x^2 + 2x - 3 = 0

x^2 + 3x - x - 3 = 0

x(x+3) - 1(x+3) = 0

(x + 3( (x - 1) = 0

x = 1 and -3

if these roots make the values of the given polynomial zero then the polynomial is divisible by the given expression

put x = 1

x^4 + 2x^3 - 2x^2 + 2x - 3

1 + 2 - 2 + 2 - 3

5 - 5

= 0

put x = -3

81 - 54 - 18 - 6 - 3

81 - 81

= 0

hence x= 1 and -3 are also the zeros of the given polynomial. So the expression is divisible by given expression.

Answer 2

Answer:

ACTUAL DIVISION PROVE X^4+2X^3-2X^2+2X-3 IS ACTAULLY DIVISIBLE BY X^2+2X-3