ANSWER:
No, the remainder is 19.
EXPLANATION:
We can check this using the remainder theorem.
"The remainder theorem is stated as follows: When a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k)."
Now, given:
- a(x) = 2x³+5x²–4x+16
- b(x) = x + 3
Equate x + 3 to 0 and solve for x.
Substitute the value of x to a(x) and solve.
- a(x) = 2x³+5x²–4x+16
- a(-3) = 2(-3)³ + 5(-3)² - 4(-3) + 16
- a(-3) = 2(-27) + 5(9) + 12 + 16
- a(-3) = -54 + 45 + 12 + 16
- a(-3) = 19
- r = 19
- The remainder is 19.
