+163 The polynomial f(x) satisfies f(x+1)−f(x)=6x+4. Find the leading coefficient of f(x)
So far, I'm convinced that f(x) is a*(6x+4)+b, but I'm stuck. I tried 6, but the leading coefficient is not 6.
All help is appreciated! Thanks!
+605 WLOG let f(x) be linear. So f(x)=ax+b. So f(x+1)=a(x−1)+b=ax−a+b→ax−a+b−ax−b=−a. Note that this is constant, so f(x) must be quadratic. Let f(x)=ax^2+bx+c. So f(x+1)=a(x+1)2+b(x+1)+c=ax2+2ax+bx+a+b+c→f(x+1)−f(x)=2ax+c⟹2a=6→a=3
