(3x+1)(x-2)+ax+b=3x^2+8x-5
work out the values of a and b

a = 13, b = - 3

Step-by-step explanation:

Expand the left side and compare like terms on both sides

(3x + 1)(x - 2) ← expand using FOIL

= 3x² - 5x - 2

left side = 3x² - 5x - 2 + ax + b ← combine like terms

             = 3x² + x(a - 5) + b - 2

right side = 3x² + 8x - 5

For the 2 sides to be equal then

a - 5 = 8 ( add 5 to both sides )

a = 13

and

b - 2 = - 5 ( add 2 to both sides )

b = - 3