19. Without actual division, prove ...
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19. Without actual division, prove that 2x–5x+ 2x -x+2 is divisible by x2-3x+2.

11th - 12th Class
Maths
Solution
123
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Please take Madam Phote of question good way [ begin{array}{l} x^{2}-3 x+2 text { divides } p(x)=2 x^{4}-5 x^{3}+2 x^{2}-x+2 end{array} ] means rasats of ( u^{2}-3 x+2=0 ) is abo the revets of ( mathrm{P}(mathrm{N}) ) [ begin{array}{l} text { 80240 } begin{array}{c} x^{2}-3 x+2=0 (x-2)(x-1)=0 x=1,2 end{array} begin{aligned} P(1)=& 2-5+2-1+2 =& 6-6 =& 6 =& 2 times 2^{4}-5 x_{2}^{3}+2 x_{2}^{2}-2+2 =& 32=40+8-2+2 =& 42-42 =& 0 end{aligned} end{array} ] thence poved, pow is is an
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