Factorise: x^3 + 13x^2 + 32x + 20 The above question is from the sureshot questions

CBSE Class 12 CBSE Class 12 Maths
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1

Factorise: x3 + 13x2 + 32x + 20

Solution:
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).
The above question is from the sureshot questions but I am not clear with the explanation.Please elaborate.Please reply urgently I have my Maths exam tomorrow

2

Factor theorem is used here
p(x) = x3+13x2+ 32x + 20
start by sub x= 1,-1,… to get p(x)=0
now
p(-1) = -1 + 13 - 32 + 20 = -33 + 33 = 0
so x+1 is a factor…factor theorem
now divide x3 + 13x3 + 32x + 20 by x+1…long division
you will get remainder zero, and quotient =x2+ 12x + 20
so,
Divident =divisor x quotient +remainder
x3+ 13x2 + 32x + 20 = (x + 1)(x2 + 12x + 20)…factorize x2 + 12x + 20 by spliting middle term