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Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

F(x) = 24x^3 + px^2 - 5x + q factors are 2x + 1 & 3x -1 let us take the factor of 2x + 1 = 0 2x = - 1 x = -1/2 apply the x value in f(x) we get f(-1/2) = 24(-1/2)^3 + p(-1/2)^2 - 5(-1/2) + q = 24 (-1/8) + p(1/4) + 5/2 + q = -3 + p(1/4) + 5/2+q = -3 +5/2+ q + p(1/4) = (-6+5)/2 + q + p (1/4) = p(1/4) +q -1/2 p(1/4) + q = 1/2 p + 4q = 4/2 p + 4q = 2 consider this as equ (1) now take the another factor 3x -1 = 0 3x = 1 x = 1/3 apply the x value in f(x) we get f(1/3) = 24 ( 1/3) ^3 + p(1/3) ^2 - 5(1/3) + q = 8 + p(1/3) - 5/3+q = p(1/3) + q + 8 - 5/3 = p (1/3) + q + (24 -5) /3 = p(1/3) + q + 19 /3 p(1/3) +q = -19/3 p + 3q = ((-19) (3) )/3 p + 3q = -19 consider it as equ (2) solving (1) & (2) we get , p + 4q = 2 p + 3q = - 19 (subtract we get ) .................................... q = 21 apply q value in any one the above equ we get p value p + 4( 21) = 2 p + 84 = 2 p = 2 -84 p =-82 therefore p is - 84