I am stuck on 2 questions. I been trying for hours but its just not working.
First question is: A quadratic equation f(x)=ax^2+bx+c, has the following properties when divided by x-1 the remainder is 4, when divided by x-2 the remainder is -3, and when divided by x+2 the remainder is 49
for the question i did long division for each and i got 4a+2b+c=-3, c-2(b-2a)=49, and c+b+a=4 from there im stuck
the second question is: when a polynomial is divided by x+2, the remainder is -10. When the same polynomial is divided by x-3, the remainder is 5. Determine the remainder when the polynomial is divided by (x+2)(x-3)
Any help is greatly appreciated. Thanks guys.