X³-6x²+11x-6 to x²-1-x² ÷
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Let p(x) = x 3 + 6x 2 + 11x + 6
Put x = – 1
p(– 1) = (– 1)3 + 6(– 1)2 + 11(– 1) + 6 = – 1 + 6 – 11 + 6 = 0
∴ (x + 1) is a factor of p(x)
So, we cam break up terms of p(x) as follows.
p(x) = x 3 + 6x 2 + 11x + 6
Therefore, the integral roots of the given equation is find out as:
p(x) = 0
⇒ (x+1)(x+2)(x+3) = 0
⇒ x = -1, -2, -3
Put x = – 1
p(– 1) = (– 1)3 + 6(– 1)2 + 11(– 1) + 6 = – 1 + 6 – 11 + 6 = 0
∴ (x + 1) is a factor of p(x)
So, we cam break up terms of p(x) as follows.
p(x) = x 3 + 6x 2 + 11x + 6
Therefore, the integral roots of the given equation is find out as:
p(x) = 0
⇒ (x+1)(x+2)(x+3) = 0
⇒ x = -1, -2, -3
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