factorise following polynomial by using factor theorem.

1}x^3_ 23x²+142x-120

2}x³-13x²-32x+20

3}2y³+y²-2y-1

1)

Let p(x) = x³ – 23x² + 142x – 120
The factors of –120 are ±1, ±2, ±3, ±4, ±5, ±6, ±8, ±10, ±12, ±15, ±20, ±24, ±30, ±60.
By hit and trial method, 

we find that p(1) = 0. So x – 1 is a factor of p(x).
Now, x³ – 23x² + 142x – 120 = x³ – x² – 22x² + 22x + 120x – 120
= x²(x –1) – 22x(x – 1) + 120(x – 1) 

=  (x – 1) (x² – 22x + 120)  [ On taking (x – 1) common]
 

Now x² – 22x + 120 can be factorised either by splitting the middle term or by using the Factor theorem. By splitting the middle term, we get
x² – 22x + 120 = x² – 12x – 10x + 120
= x(x – 12) – 10(x – 12)
= (x – 12) (x – 10)
So, x³ – 23x² – 142x – 120 = (x – 1)(x – 10)(x – 12)

2) 

Let p(x) = x³-13x²-32x+20

The given polynomial can't be factorized because it has no rational zeros.

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