Without actual division. prove that $2 x^{4} - 5 x^{3} + 2 x^{2} - x + 2$ is divisible by $x^{2} - 3 x + 2$

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Solution

$∵ P (x) = 2 x^{4} - 5 x^{3} + 2 x^{2} - x + 2 a n d x^{2} - 3 x + 2 = (x - 1) (x - 2) l e t x^{2} - 3 x + 2 i s t h e f a c t o r o f P (x) t h e n, x^{2} - 3 x + 2 = 0 \Rightarrow (x - 1) (x - 2) = 0 \Rightarrow x = 1 a n d 2 f o r x = 1 P (1) = 0 a n d f o r x = 2 P (2) = 0 ∵ P (1) = P (2) = 0 ∴ P (x) i s d i v i s i b l e b y x^{2} - 3 x + 2$

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Similar questions

2 x^{4} - 5 x^{3} + 2 x^{2} - x + 2

x^{2} - 3 x + 2

2 x^{4} - 5 x^{3} + 2 x^{2} - x + 2

x^{2} - 3 x + 2

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a

x^{4} + {2 x}^{3} - {2 x}^{2} + 2 x - 3

x^{2} + 2 x - 3

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