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find the integral zeroes of the polynomial 2x³ +5x² - 5x-2

$L e t t h e p o l y n o m i a l f (x) = 2 x^{3} + 5 x^{2} - 5 x - 2 T o f i n d t h e int e g r a l z e r o e s, w r i t e t h e p r i m e f a c t o r o f c o n s \tan t t e r m 2. i . e ., \pm 1, \pm 2 N o w, W h e n x = - 1 f (- 1) = 2 {(- 1)}^{3} + 5 {(- 1)}^{2} - 5 (- 1) - 2 \Rightarrow f (- 1) = - 2 + 5 + 5 - 2 = 6 \Rightarrow f (- 1) \neq 0 T h u s, x = - 1 i s n o t t h e z e r o o f g i v e n p o l y n o m i a l W h e n x = 1 f (1) = 2 {(1)}^{3} + 5 {(1)}^{2} - 5 (1) - 2 \Rightarrow f (1) = 2 + 5 - 5 - 2 = 6 \Rightarrow f (1) = 0 T h u s, x = 1 i s t h e z e r o o f g i v e n p o l y n o m i a l W h e n x = - 2 f (- 2) = 2 {(- 2)}^{3} + 5 {(- 2)}^{2} - 5 (- 2) - 2 \Rightarrow f (- 2) = - 16 + 20 + 10 - 2 = 12 \Rightarrow f (- 2) \neq 0 T h u s, x = - 2 i s n o t t h e z e r o o f g i v e n p o l y n o m i a l W h e n x = 2 f (2) = 2 {(2)}^{3} + 5 {(2)}^{2} - 5 (2) - 2 \Rightarrow f (2) = 16 + 20 - 10 - 2 = 24 \Rightarrow f (2) \neq 0 T h u s, x = 2 i s n o t t h e z e r o o f g i v e n p o l y n o m i a l H e n c e, o n l y x = 1 i s t h e int e g r a l z e r o o f g i v e n p o l y n o m i a l$

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