The expression #10x^2-x-24# can be written as #(Ax-8)(Bx+3)#, where #A# and #B# are integers. What is #AB + B#?

Question from AoPS. Please help :)

1 Answer
Jun 7, 2018

#AB+B=12, 65/8#

Explanation:

.

#10x^2-x-24=(Ax-8)(Bx+3)#

#10x^2-x-24=ABx^2+3Ax-8Bx-24#

#10x^2-x-24=ABx^2-(8B-3A)x-24#

#AB=10#

#8B-3A=1, :. 8B=1+3A, B=(1+3A)/8#

#(A(1+3A))/8=10#

#3A^2+A-80=0#

#A=(-1+-sqrt(1-4(3)(-80)))/6=(-1+-sqrt961)/6=(-1+-31)/6#

#A=5, -16/3#

#A=5, :. B=2, :. AB+B=10+2=12#

#A=-16/3, :. B=-15/8, :. AB+B=10-15/8=65/8#