Question

Using the factor theorem, factorise x^3-2x^2-5x+6
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Answer 1

Answer:

x³ - 2x² - 5x + 6

Step-by-step explanation:

Let x be 1

P(x) = x³ - 2x² - 5x + 6

= (1)³ - 2(1)³ - 5(1) + 6

= 1 - 2 - 5 + 6

= 7 - 7

= 0

x - 1 is a factor.

Step-by-Step explanation:

x³ - 2x² - 5x + 6

= x³ - x² - x² + x -6x + 6

= ( x - 1 ) ( x² - x - 6 )

= ( x - 1 ) { x² - 3x + 2x - 6 }

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

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

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