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Factorize x3-2x2-5x+6

The given polynomial is f(x) = x 3 – 2x 2 – 5x + 6.

Putting x = 1 in f(x), we have

f(1) = (1)3 – 2(1)2 – 5 × 1+ 6 = 1 – 2 – 5 + 6 = 0

By factor theorem, (x – 1) is the factor of f(x).

Dividing f(x) by (x – 1), we have



So, x = 1 , 3 or -2

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  • 35
View Full Answer

 Let x-1 be a factor of x3-2x2-5x+6

putting x= 1

x(1) = (1)³ - 2(1)² - 5(1) + 6

x(1) = 1 - 2 -5 +6

x(1)= 7 - 7

x(1) = 0

Now x3-2x2-5x+6 divided by (x - 1)

It gives you x² - x - 6

Now, x² - x - 6 (x-1)

= x² + 2x - 3x - 6 (x-1)

= x ( x+2) -3 (x+2) (x-1)

= (x-3) (x+2) (x-1)

 

Hope it Helped ......................

  • 10

thnk u

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