Question 233605
express 3x²+24x+1 in the form a(x+b)²+c
.
We are basically trying to "complete the square":
{{{3x^2 + 24x + 1}}}
Group the x terms:
{{{(3x^2 + 24x) + 1}}}
Factor so that the x^2 has no coefficient:
{{{3(x^2 + 8x) + 1}}}
Now, you are looking for the term to complete square (1/2 'b' then square it):
{{{3(x^2 + 8x + ___ ) + 1}}}
{{{3(x^2 + 8x + 16 ) + 1 - 16}}}
{{{3(x^2 + 8x + 16 ) - 15}}}
{{{3(x+4)^2 - 15}}}