Question

Which polynomial has (x+1) as a factor?

a) x^3+2x^2−19x−20
b) x^3−21x+20
c) x^3+8x^2+11x−20
d) x^3−3x^2+3x−1

Answer 1

To determine which polynomial has (x+1) as a factor, we can check if substituting -1 for x in each option results in zero. Option a) x^3+2x^2−19x−20 satisfies this condition.

Step-by-step explanation:

To determine which polynomial has (x+1) as a factor, we can check if substituting -1 for x in each answer choice results in zero. Let's do that for each option:

1. Option a) (-1)^3 + 2(-1)^2 - 19(-1) - 20 = -1 + 2 + 19 - 20 = 0. So, (x+1) is a factor of option a).
2. Option b) (-1)^3 - 21(-1) + 20 = -1 + 21 + 20 = 40. So, (x+1) is not a factor of option b).
3. Option c) (-1)^3 + 8(-1)^2 + 11(-1) - 20 = -1 + 8 - 11 - 20 = -24. So, (x+1) is not a factor of option c).
4. Option d) (-1)^3 - 3(-1)^2 + 3(-1) - 1 = -1 + 3 - 3 - 1 = -2. So, (x+1) is not a factor of option d).

Therefore, the correct answer is option a) x^3+2x^2−19x−20, as (x+1) is a factor.