Question 171705
It looks like they want you to factor the equations
{{{y = x^2 - 5x + 6}}}
Look at the constant term, {{{6}}}
Notice that {{{(-2)*(-3) = 6}}} and {{{-2 + (-3) = -5}}}
{{{y = (x - 2)(x - 3)}}} answer
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{{{y = x^2 + 2x - 1}}}
A good method is the "complete the square" method
Set {{{y = 0}}} to find the roots
Take 1/2 of the coefficient of {{{x}}}, square it
and add it to both sides
First, though, add {{{1}}} to both sides
{{{1 = x^2 + 2x}}}
{{{1 + (2/2)^2 = x^2 + 2x + (2/2)^2}}}
{{{2 = x^2 + 2x + 1}}}
{{{2 = (x + 1)^2}}}
Take the square root of both sides
{{{sqrt(2) = x + 1}}}
The roots of the equation are:
{{{x = -1 + sqrt(2)}}} and
{{{x = -1 - sqrt(2)}}}
The factors of the equation are
{{{(x + 1 - sqrt(2))(x + 1 + sqrt(2))}}}
Note that the factors are just {{{x - r[1]}}} and {{{x - r[2]}}}
where {{{r[1]}}} and {{{r[2]}}} are the roots