Question

Which of the following is a polynomial with roots 4, −5, and 7?

Question 4 options:

1) f(x) = x3 − 6x2 − 27x + 140
2) f(x) = x3 − 6x2 − 20x + 27
3) f(x) = x3 − 20x2 − 27x + 35
4) f(x) = x3 − 20x2 − 35x + 140

Answer 1

Answer: 1) f(x) = x3 − 6x2 − 27x + 140

Which of the following is a polynomial with roots 4, −5, and 7?

Question 4 options:

1) f(x) = x3 − 6x2 − 27x + 140

2) f(x) = x3 − 6x2 − 20x + 27

3) f(x) = x3 − 20x2 − 27x + 35

4) f(x) = x3 − 20x2 − 35x + 140

Explanation:

I just did the assignment and the correct answer was 1). f(x) = x3 − 6x2 − 27x + 140. Hope this helps.

Good Luck!!

Answer 2

If x = 4, then the factor is (x - 4); if x = -5, then the factor is (x + 5); if x = 7, then the factor is (x - 7). We need to FOIL all these together to get a third degree polynomial. (x - 4)(x + 5) = (x^2 + x - 20). Now multiply that by (x- 7): (x^2+x-20)(x-7) =
`x^3+x^2-20x-7x^2-7x+140`. Combine like terms to get
`x^3-6x^2-27x+140`, the first choice above.