Question

Consider this polynomial. p(x) = 3×3 + 11×2 – 4x – 6
Which statements are true?

A. The quotient of p(x) & (x + 2) is 3x^2 + 5x + 6 + 6/x + 2
B. (x + 2) is a factor of p
C. p(-2) = 22
D. p(-2) = 6
E. The quotient of p(x) & (x + 2) is 3x^2 + 5x – 14 + 22/x + 2

1. diemkieu
The correct options about the given polynomial are; C. p(-2) = 22 and
E. The quotient of p(x) & (x + 2) is 3x^2 + 5x – 14 + 22/x + 2

### How to carry out Polynomial Division?

The general form of equation of a Polynomial is ax² + bx + c.
where;
a, b, and c are real numbers with a ≠ 0,
The degree of a polynomial is the highest exponent of the variable in the polynomial.
Option C) Calculation for p(-2)
To get the value of p(-2), at the place of ‘x’ put (-2) in the polynomial p(x).
p(x) = 3x³ + 11x² – 4x – 6
p(-2) = 3(-2)³ + 11(-2)² – 4(-2) – 6
p(-2) = 22
Thus, option C is correct and option D is incorrect.
A) To calculate the quotient divide the polynomial p(x) by (x +2)
The solution of this is attached in the file.
Therefore, option E is correct and option A is incorrect.
As, we can see from the division of polynomial p(x) by (x + 2) , the p(x) polynomial is not completely divisible by (x +2). Therefore, option B is also incorrect.