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x-1 is a factor of which of the following?

{:[" I. "x^(2)+x-2],[" II. "2x^(2)-5x+3]:}
Neither
I only
Il only
| and II

x1x-1 is a factor of which of the following?\newlineI. x2+x2x^2+x-2\newlineII. 2x25x+32x^2-5x+3\newlinea) Neither\newlineb) I only\newlinec) II only\newlined) I and II

Full solution

Q. x1x-1 is a factor of which of the following?\newlineI. x2+x2x^2+x-2\newlineII. 2x25x+32x^2-5x+3\newlinea) Neither\newlineb) I only\newlinec) II only\newlined) I and II
  1. Understand the problem: Step 11: Understand the problem.\newlineWe need to find out if x1x-1 is a factor of the given polynomials.
  2. Check factor x1x-1: Step 22: Check if x1x-1 is a factor of x2+x2x^2 + x - 2. Use the factor theorem: if x1x-1 is a factor, then substituting x=1x = 1 should make the polynomial equal to zero. Substitute x=1x = 1 into x2+x2x^2 + x - 2: 12+12=1+12=01^2 + 1 - 2 = 1 + 1 - 2 = 0.

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