Without actual division, show that (x3 – 3x2 – 13x + 15) is exactly divisible by (x2 + 2x - 3).

Let’s find the roots of the equation (x2 + 2x - 3)

x2 + 3x x – 3 = 0


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


(x + 3) (x – 1)


Hence, if (x + 3) and (x – 1) satisfies the equation x3 – 3x2 – 13x + 15 = 0, then (x3 – 3x2 – 13x + 15) will be exactly divisible by (x2 + 2x - 3).


For x = -3,


(-3)3 3(-3)2 13(-3) + 15


-27 27 + 39 + 15 = 0


For x = 1,


13 3(1)2 13(1) + 15


1 3 13 + 15 = 0


Hence proved.


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