To determine if (x-1) is a factor of the given polynomials, we can use the Remainder Theorem. We substitute x = 1 into each polynomial and check if the result is zero.
a) For the polynomial 2x^3 + 5x^2 + x + 2: Substituting x = 1, we get: 2(1)^3 + 5(1)^2 + 1 + 2 = 2 + 5 + 1 + 2 = 10
Since the result is not zero, (x-1) is not a factor of the polynomial 2x^3 + 5x^2 + x + 2.
b) For the polynomial 4x^3 + 5x^2 - 3x + 6: Substituting x = 1, we get: 4(1)^3 + 5(1)^2 - 3(1) + 6 = 4 + 5 - 3 + 6 = 12
Again, the result is not zero, so (x-1) is not a factor of the polynomial 4x^3 + 5x^2 - 3x + 6.
Therefore, neither of the polynomials has (x-1) as a factor. Let me know if you have any more questions!
Answers & Comments
Answer:
B is the correct answer .
please marks be brainliest .
To determine if (x-1) is a factor of the given polynomials, we can use the Remainder Theorem. We substitute x = 1 into each polynomial and check if the result is zero.
a) For the polynomial 2x^3 + 5x^2 + x + 2:
Substituting x = 1, we get:
2(1)^3 + 5(1)^2 + 1 + 2 = 2 + 5 + 1 + 2 = 10
Since the result is not zero, (x-1) is not a factor of the polynomial 2x^3 + 5x^2 + x + 2.
b) For the polynomial 4x^3 + 5x^2 - 3x + 6:
Substituting x = 1, we get:
4(1)^3 + 5(1)^2 - 3(1) + 6 = 4 + 5 - 3 + 6 = 12
Again, the result is not zero, so (x-1) is not a factor of the polynomial 4x^3 + 5x^2 - 3x + 6.
Therefore, neither of the polynomials has (x-1) as a factor. Let me know if you have any more questions!