Question

Factories x^3-23x^2+142x-120 and full explain ​

Answer 1

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Answer:

⇒ (x - 1) (x - 12) (x - 10)

Step-by-step explanation:

Let p(x) = x^3 - 23x² + 142 - 120

We shall now look look for all other factors of - 120. Some of these are ±1, ±2, ±3, ±4 , ±5, ±6, ±7, ±8, ±9, ±10....

By trial, we find that p(1) = 0.

So, x - 1 is a factor of p(x).

Now, we see that ;

⇒ x^3 - 23x² + 142 - 120

⇒ x^3 - x² - 22x² + 22x + 120x - 120

⇒ x²( x - 1) - 22x (x - 1 ) + 120(x - 1)

⇒ (x - 1) (x² - 22x + 120)

⇒ (x - 1) (x² - 10x - 12x + 120)

⇒ (x - 1) [x( x - 10 ) - 12( x - 10 )

⇒ (x - 1) (x - 12) (x - 10)