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 =

$(-\frac{1}{2})^2=\frac{1}{4}$

So, we will substitute:

$\begin{gathered} u=x-\frac{1}{4} \\ so,x=u+\frac{1}{4} \end{gathered}$

The substitution into the expression will be as follows:

$undefined$