Question

If the coefficient of x^2 in the expansion of (ax+3)(x^2+6x-5) is -3, then the remainder when the expansion is divided by (x-1) is...?

Answer 1

did you expand out the product and figure out what a is ?

Answer 2

I would multiply the expression to get
\[ ax^3 +6ax^2 -5ax + 3x^2 +18x-15 \\
ax^3 + (6a+3)x^2 + (18-5a) x -15\]
the coefficient of x^2 is -3
that means
6a+3 = -3
or
a= -1

replace a with -1 in the expansion:
\[ -x^3 -3x^2 +23 x -15 \]
now divide by (x-1) and find the remainder.
the easiest way , if you know it, is to use synthetic division