If $x^{3} + 13 x^{2} + 32 x + 20 = (x + a) (x + b) (x + c)$ .Find $a + b + c$

13

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Solution

The correct option is B $13$
$x^{3} + 13 x^{2} + 32 x + 20 w e c a n c l e a r l y s e e x = - 1 i s o n e o f t h e z e r o e s o f t h e g i v e n p o l y n o m i a l ∴ = (x + 1) (x^{2} + 12 x + 20) = (x + 1) [x^{2} + 10 x + 2 x + 20] = (x + 1) [x (x + 10) + 2 (x + 10)] = (x + 1) (x + 10) (x + 2) c o m p a r e i t w i t h (x + a) (x + b) (x + c) w e g e t a = 1, b = 10, c = 2 ∴ a + b + c = 1 + 10 + 2 = 13$

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Factories:
$x^{3} + 13 x^{2} + 32 x + 20$

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