Factorize the polynomial f=x^3+4x^2-7x-10

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We have to factorize f=x^3 + 4x^2 - 7x - 10

f=x^3 + 4x^2 - 7x - 10

=> x^3 + 6x^2 - 2x^2 + 5x - 12x - 10

=> x^3 + 6x^2 + 5x - 2x^2  - 12x - 10

=> x(x^2 + 6x +5) - 2(x^2 +...

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We have to factorize f=x^3 + 4x^2 - 7x - 10

f=x^3 + 4x^2 - 7x - 10

=> x^3 + 6x^2 - 2x^2 + 5x - 12x - 10

=> x^3 + 6x^2 + 5x - 2x^2  - 12x - 10

=> x(x^2 + 6x +5) - 2(x^2 + 6x + 5)

=> (x - 2) ( x^2 + 6x +5)

=> (x - 2)(x^2 + 5x +x +5)

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

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

Therefore x^3 + 4x^2 - 7x - 10 = (x - 2)(x +5) (x +1)

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