Expressions Is it a possible expression for p
A. 3x(x-4)(x+ 2/3 )(x+9) Yes
B. -x(x+4)(x+ 2/3 )(x-9) Yes
c. -3x(x+4)(3x+2)(x-9) Yes
D. 3x(x+4)(2x-3)(x-9) Yes
E. -3x(x+4)(3x+2)(x-9)^2 Yes .
To determine if each expression is a possible expression for p, we need to look at the factors and check for consistency in the signs and whether the degree of each factor matches the degree of p.
Let's analyze each option:
A. 3x(x−4)(x+ 2/3 )(x+9)
This is a valid expression for p as it consists of linear factors and the degrees are consistent.
B. −x(x+4)(x+ 2/3 )(x−9)
This is also a valid expression for p as it consists of linear factors, and the signs are consistent.
C. −3x(x+4)(3x+2)(x−9)
This is a valid expression for p as it consists of linear factors, and the signs are consistent.
D. 3x(x+4)(2x−3)(x−9)
This is a valid expression for p as it consists of linear factors, and the signs are consistent.
E. −3x(x+4)(3x+2)(x−9) ^2
This is also a valid expression for p as it consists of linear factors, and the signs are consistent. Note that there is a square term (x−9)^2
So, all options (A, B, C, D, and E) are possible expressions for p.
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 expressions that could represent p.
A. 3x(x-4)(x+ 2/3 )(x+9)
B. -x(x+4)(x+ 2/3 )(x-9)
C. -3x(x+4)(3x+2)(x-9)
D. 3x(x+4)(2x-3)(x-9)
E. -3x(x+4)(3x+2)(x-9)^2