Question

2x^4-5x^3+2x^2-x+2/x^​

Answer 1

Answer:

Let p(x) = 2x4 – 5x3 + 2x2 – x + 2 firstly, factorise x2 - 3x + 2. Now, x2 - 3x + 2 = x2 - 2x - x + 2 [by splitting middle term] = x(x-2)-1 (x-2) = (x-1)(x-2) Hence, 0 of x2-3x+2 are land 2. We have to prove that, 2x4 – 5x3 + 2x2 – x+ 2 is divisible by x2-3x+2 i.e., to prove that p (1) =0 and p(2) =0 Now, p(1) = 2(1)4 – 5(1)3 + 2(1)2 -1 + 2 = 2 - 5 + 2 - 1 + 2 = 6 - 6 = 0 and p(2) = 2(2)4 – 5(2)3 + 2(2)2 – 2 + 2 = 2x16 - 5x8 + 2x4 + 0 = 32 – 40 + 8 = 40 – 40 = 0 Hence, p(x) is divisible by x2 - 3x + 2.

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