Question

x³-7x-6

Answer 1

\(x^3-7x-6\)

\(=x^3-x-6x-6\)

\(=x\left(x^2-1\right)-6\left(x+1\right)\)

\(=x\left(x+1\right)\left(x-1\right)-6\left(x+1\right)\)

\(=\left(x+1\right)\left[x\left(x-1\right)-6\right]\)

\(=\left(x+1\right)\left(x^2-x-6\right)\)

\(=\left(x+1\right)\left(x^2-3x+2x-6\right)\)

\(=\left(x+1\right)\left[x\left(x-3\right)+2\left(x-3\right)\right]\)

\(=\left(x+1\right)\left(x+2\right)\left(x-3\right)\)

Answer 2

\(x^3-7x-6\\ =x^3-9x+2x-6\\ =\left(x^3-9x\right)+\left(2x-6\right)\\ =x\left(x^2-9\right)+2\left(x-3\right)\\ =x\left(x+3\right)\left(x-3\right)+2\left(x-3\right)\\ =\left(x^2+3x\right)\left(x-3\right)+2\left(x-3\right)\\ =\left(x^2+3x+2\right)\left(x-3\right)\\ =\left(x^2+2x+x+2\right)\left(x-3\right)\\ =\left[\left(x^2+2x\right)+\left(x+2\right)\right]\left(x-3\right)\\ =\left[x\left(x+2\right)+\left(x+2\right)\right]\left(x-3\right)\\ =\left(x+1\right)\left(x+2\right)\left(x-3\right)\)

Answer 3

c1 . x³ - 7x - 6

= x³ - 7x + 8 - 14

= ( x + 2)( x² - 2x + 4) - 7( x + 2)

= ( x + 2)( x² - 2x - 3)

= ( x + 2)( x² + x - 3x - 3)

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

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

c2. x³ - 7x - 6

= x³ - x - 6x - 6

= x( x² - 1) - 6( x + 1)

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

= ( x + 1)( x² - x - 6)

= ( x + 1)( x² + 2x - 3x - 6)

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

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

c3 . x³ - 7x - 6

= x³ + x² - x² - 7x - 6

= x²( x + 1) - ( x² + 7x + 6)

= x²( x + 1) - ( x² + x + 6x + 6)

= x²( x + 1) - [ x( x + 1) + 6( x + 1) ]

= x²( x + 1) - ( x + 1)( x + 6)

= ( x + 1)( x² - x - 6)

= ( x + 1)( x² + 2x - 3x - 6)

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

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

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