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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

Respuesta :

Luv2Teach
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) = [tex]x^3+x^2-20x-7x^2-7x+140[/tex].  Combine like terms to get  [tex]x^3-6x^2-27x+140[/tex],  the first choice above.

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

Step-by-step explanation:

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

Good Luck!!

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