Factorise x^3+13x^2+32x+20
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Yogita Ingle 4 years, 3 months ago
Let p(x) = x3 + 13x2 + 32x + 20
p(-1) = -1 + 13 - 32 + 20 = -33 + 33 = 0
Therefore (x + 1) is a factor of p(x).
On dividing p(x) by (x + 1) we get
p(x)
(x + 1) = x2 + 12x + 20
Thus,
x3 + 13x2 + 32x + 20 = (x + 1)(x2 + 12x + 20)
= (x + 1) (x2 + 10x + 2x + 20)
= (x + 1)[x(x + 10) + 2(x + 10)]
= (x + 1) (x +2) (x + 10)
Hence, x3 + 13x2 + 32x + 20 = (x + 1) (x +2) (x + 10).
1Thank You