Question

Check by division algorithm whether x2−2 is a factor of x4+x3+x2−2x−3.
A) True
B) False

Answer 1

To check whether x^2 - 2 is a factor of x^4 + x^3 + x^2 - 2x - 3, perform polynomial long division. The remainder will determine if it is a factor or not. In this case, the remainder is not zero, so x^2 - 2 is not a factor.

Step-by-step explanation:

To check whether x2 - 2 is a factor of x4 + x3 + x2 - 2x - 3, we can divide the given polynomial by the supposed factor:

x4 + x3 + x2 - 2x - 3

÷ x2 - 2

To do this, we use polynomial long division. Divide the leading term of the dividend (x4) by the leading term of the divisor (x2) to get x2. Multiply the divisor (x2 - 2) by the result (x2) to get x4 - 2x2. Subtract this from the dividend to obtain the remainder: 3x2 - 2x - 3. Since the remainder is NOT zero, x2 - 2 is NOT a factor of x4 + x3 + x2 - 2x - 3. Therefore, the answer is B) False.