Find the value of q. Please Show Steps

Question

-6x³ - 7x² + qx - 12 is divisible by 3x – 4. Find the value of q. Justify your answer by showing your work.

Answer 1

3x-4 divided into -6x^3 -7x^2+qx -12

use long division

quotient =-2x^2-5x+(q-20)/3 = -2x^2-5x+3

since -4(q-20)/3=-12 if the remainder =0

q-20=3(12/4)=3(3)=9

q=9+20=29

divisor times quotient = dividend:

(3x-4)(-2x^2-5x+3)=-6x^3+8x^2-15x^2 +20x+9x-12 = dividend

= -6x^3-7x^2+29x-12

q= 29, for zero remainder

do the algebraic long division very similar to arithmetic long division

at the last step you get -12 minus (4/3)(q-20), set that equal to zero and solve for q