Question

If $f\left(x\right)=2x^3-13x^2+10x-19$, find the value of $f(x-1)$.

Answer 1

$f\left(x\right)=2x^3-13x^2+10x-19$

$f(x-1)=2(x-1{)}^3-13(x-1{)}^2+10(x-1)-19$

$=2(x^3+(\frac{3}{1})\cdot x^2\cdot (-1)+(\frac{3}{2})\cdot x\cdot (-1{)}^2+(\frac{3}{3})\cdot (-1{)}^3)$

$-13(x^2+(\frac{2}{1})\cdot x\cdot (-1)+(\frac{2}{2})\cdot (-1{)}^2)+10(x-1)-19$

$=2(x^3-3x^2+3x-1)-13(x^2-2x+1)+10(x-1)-19$

$=2x^3-19x^2+42x-44$