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.

• x + 3 = 0
• x = -3

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.