Question

I need help with number 40. Using substitution to factor a polynomial

Answer 1

Given the expression number 40:

`x^2-x-1`

we will use the substitution to factor the polynomial

To find the suitable substitution, find the factor which will be used to make a complete square, the factor will be = (coefficient of x/2)²

So, the factor will be =

`(-(1)/(2))^2=(1)/(4)`

So, we will substitute:

`\begin{gathered} u=x-(1)/(4) \\ so,x=u+(1)/(4) \end{gathered}`

The substitution into the expression will be as follows: