Question

The polynomial 2x³ + qx² + rx + 2 has a

factor (x - 1) and leaves a remainder of
12 when divided by (x - 2). Find the
constants q and r and hence the other
factors of the polynomial.​

Answer 1

q = 1 , r = -5

other factors of polynomial:

(2x - 1) & (x + 2)

Explanation:

In the first part, substitute x = 1 make it equal to 0.

Substitute x = 2 and make it equal to 12.

Rearrange both, until you have two linear equations.

Solve the set of simultaneous equation to find q and r .

Second part place the value of q and r to have the full polynomial.

Carry out long division, dividing the polynomial by the factor that's stated in the question (x - 1) and you will have a quadratic equation.

Factorise the quadratic equation to have the two other factors of the polynomial.

Hope this helps:))