Question

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Answer 1

Step-by-step explanation:

x^2 - 3x + 2

= x^2 - 2x - x + 2

= x(x - 2) - 1(x - 2)

= (x-1)(x-2)

p(x) = 2x^4 - 5x^3 + 2x^2 - x + 2

When p(x) is divided by x-1, then remainder = p(1)

p(1) = 2(1)^4 - 5(1)^3 + 2(1)^2 - 1 + 2

      = 2 - 5 + 2 - 1 + 2 = 0

When p(x) is divided by x-2, then remainder = p(2)

p(2) = 2(2)^4 - 5(2)^3 + 2(2)^2 - 2 + 2

       = 32 - 40 + 8 - 2 + 2 = 0

Since polynomial p(x) is divisible by the factors of x^2 - 3x + 2, then x^2 - 3x + 2 will exactly dive polynomial p(x).

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