given that x-3 and 2x+1 are factors of 2x^3 + px^2 + (2q-1)x + Q :

Question

A) FIND THE VALUE OF P AND THE VALUE OF Q.

B) EXPLAIN WHY X+2 IS ALSO A FACTOR OF THE EXPRESSION.

Answer 1

p =-1, q=-6

(x+2)(x-3)(2x+1) = 2x^3 -x^2 -13x -6

=2x^3 +px + (2q-1)x + q

match the coefficients:

2=2 for x^3

-1 = p for x^2

2q-1 = -13 for x

q =-6 for the constant term

q = -6, p = -1 2q-1 =-13, 2q= -12, q=-12/2