Expressions A. (-3x(x + 4)(3x + 2)(x - 9)) and E. (-3x(x + 4)(3x + 2)(x - 9)^2) match zeros at -4, -2/3, 0, and 9.
To determine the expression that could represent the polynomial function p(x) with zeros at -4, -2/3, 0, and 9, consider the factors in each expression.
Given zeros at -4, -2/3, 0, and 9, the factors in the expression must reflect these roots.
Let's analyze each expression:
A. -3x(x + 4)(3x + 2)(x - 9)
This expression contains factors that produce zeros at -4, -2/3, and 9, matching three of the given zeros.
B. 3x(x – 4)(x + 3)(x +9)
This expression does not contain factors that generate zeros at -2/3 and 0. It doesn't match all four zeros.
C. 3x(x + 4)(2x - 3)(x -9)
This expression generates zeros at -4, 3/2 (from \(2x - 3\)), and 9. It doesn't match the zero at -2/3 or 0.
D. - x(x + 4) (x + })(x – 9)
This expression doesn't match the zero at -2/3. It generates zeros at -4, 0 (from \(x + 3\)), and 9.
E. -3x(x + 4)(3x + 2)(x - 9)^2
Similar to option A, this expression generates zeros at -4, -2/3, and 9, consistent with three of the given zeros.
Therefore, expressions A and E could represent the polynomial \( p(x) \) with zeros at -4, -2/3, 0, and 9. These expressions produce factors corresponding to all four given zeros.
Question:
The polynomial p is a function of x. The graph of p has four zeros at -4, -2/3, 0, and 9
Select all the expression that could represent p.
A. -3x(x + 4)(3x + 2)(x - 9)
B. 3x(x – 4) (x + 3)(x +9)
с. 3x(x + 4)(2x - 3)(x -9)
D. - x(x + 4) (x + })(x – 9)
E. -3x(x + 4)(3x + 2)(x - 9)2