1) Given that p(-3), p(-1), and p(5)=0, which expression could be p(x)?
A)x^3-x^2-17x-15
B)x^3+x^2-17x+15
C)x^3-3x^2-13x+15
D)x^3-9x^2+23x-15
Hi Steve, I got what you said, but how would I solve this equation then?
Oh never mind! So the answer would be B?
right on
To solve this equation, we need to find the expression that satisfies the given conditions. Let's plug in the values of -3, -1, and 5 into each option and see which one gives us 0 for all the values.
A) If we plug in -3 into option A, we get (-3)^3 - (-3)^2 - 17(-3) - 15 = -27 - 9 + 51 - 15 = 0. So, this option is a possible solution.
B) If we plug in -3 into option B, we get (-3)^3 + (-3)^2 - 17(-3) + 15 = -27 + 9 + 51 + 15 = 48. Since this is not 0, option B is not the correct solution.
C) If we plug in -3 into option C, we get (-3)^3 - 3(-3)^2 - 13(-3) + 15 = -27 - 27 + 39 + 15 = 0. So, this option is a possible solution.
D) If we plug in -3 into option D, we get (-3)^3 - 9(-3)^2 + 23(-3) - 15 = -27 - 81 - 69 - 15 = -192. Since this is not 0, option D is not the correct solution.
Now, repeat the same process for -1 and 5 by plugging them into options A, C, and D. You will find that option C satisfies all the values and gives us 0 for each of them. Therefore, the correct expression for p(x) is option C, which is x^3 - 3x^2 - 13x + 15.