[Video] Q10: Ax^3 + bx^2 + cx + d = 0 in the equation above, a, b, c, and d are constants. if the equation has roots −1, −3, and 5, which of the following is a factor of ax^3 bx^2 cx d?

Explanation for Question 10 From the Math (No Calc) Section on the Official Sat Practice Test 7

Question 10 says in the equation above a, 2 B, C, and D are constants. 3 If the equation has roots, negative one, 4 negative three and five, which of the following is a factor of a X 5 cubed plus B X squared plus C X plus D. 6 So when you're giving roots, you can find the factors of an equation by 7 taking X plus the opposite of the root. 8 So for example, if the root is negative one, 9 you know that the factor is X plus positive one, 10 the opposite of negative one. Now, 11 the reason why that's true is because the factor has to equal zero when 12 the root is input into the equation. 13 So when I plug negative one into this equation, 14 I get negative one plus one, and that becomes zero. 15 And that's what a root is. It's an X value that when plugged in, 16 gives a Y value of zero. So to find the answer to this question, 17 all we have to do is take these roots and rewrite them as X 18 plus the opposite of the zeros. 19 So we already came up with X plus one. 20 We know another factor is X plus positive three, 21 and that's the third factor is X plus negative five or 22 X minus five. And from that, 23 we know that the answer here is being, because that's the only factor that 24 we've written out here that's included, 25 right?