Question

The leading coefficient of a cubic polynomial P is 2, and the coefficient of the linear term is -5. If P(0) = 7 and P(2) = 21, find P(3).

a) 35
b) 41
c) 47
d) 53

Answer 1

To find P(3), substitute x = 3 into the cubic polynomial equation P(x) = 2x^3 - 3x^2 - 4x + 7.

Step-by-step explanation:

To find P(3), we need to determine the equation of the cubic polynomial P. Given that the leading coefficient is 2 and the coefficient of the linear term is -5, we can start with the general form of a cubic polynomial:

P(x) = ax^3 + bx^2 + cx + d

Using the information provided, we can set up a system of equations to solve for the coefficients. Plugging in P(0) = 7 and P(2) = 21:

7 = d

21 = 8a + 4b + 2c + d

Solving this system, we find a = 3, b = -3, and c = -4. Therefore, P(x) = 2x^3 - 3x^2 - 4x + 7. To find P(3), we substitute x = 3 into the equation:

P(3) = 2(3)^3 - 3(3)^2 - 4(3) + 7 = 47