x^3+13x^2+32x+20
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Preeti Dabral 3 years, 3 months ago
Let p(x) = x3 + 13x2+ 32x + 20
p(-1) = (-1)3 + 13(-1)2 + 32(-1) + 20
= -1 + 13 - 32 + 20 = 0
∴ By Factor Theorem, x - (-1), i.e., (x + 1) is a factor of p(x).
x3 + 13x2 + 32x + 20
= x2(x + 1) + 12x(x + 1) + 20(x + 1)
= (x + 1)(x2 + 12x + 20)
= (x + 1)(x2 + 2x + 10x + 20)
= (x + 1){x(x + 2) + 10(x + 2)}
= (x + 1)(x + 2)(x + 10).
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