Respuesta :
Complete question is;
Which of the number(s) below are potential roots of the function? p(x) = x⁴ + 22x² – 16x – 12
A) ±6
B) ±1
C) ±3
D) ±8
Answer:
Options A, B & C: ±6, ±1, ±3
Step-by-step explanation:
We are given the polynomial;
p(x) = x⁴ + 22x² – 16x – 12
Now, the potential roots will be all the rational numbers equivalent of p/q.
Where;
p are the factors of the constant term of the polynomial
q are the factors of the leading coefficient of the polynomial
Now, in the given polynomial, the constant term is seen as -12 while leading coefficient is 1 which is the coefficient of x⁴.
We know that factors of 12 are any of:
±1, ±2, ±3, ±4, ±6 and ±12
While possible factors of 1 is just ±1.
Thus, all the potential roots of the polynomial function are;
±1, ±2, ±3, ±4, ±6 and ±12
From the options given, option A, B & C could be the potential roots.
