Question 344364
{{{2w^2-7w+6=(2w+a)(w+b)}}}
{{{2w^2-7w+6=2w^2+2bw+aw+ab}}}
{{{2w^2-7w+6=2w^2+(2b+a)w+ab}}}
Comparing,
1.{{{2b+a=-7}}}
2.{{{ab=6}}}
To satisfy eq. 1, both {{{a}}} and {{{b}}} must be negative.
Look at factors of 6, they must satisfy eq. 1 also,
{{{a=-6}}},{{{b=-1}}},{{{2b+a=-2-6=-8}}}
{{{a=-3}}},{{{b=-2}}},{{{2b+a=-4-3=highlight(-7)}}}
{{{a=-2}}},{{{b=-3}}},{{{2b+a=-6-2=-8}}}
{{{a=-1}}},{{{b=-6}}},{{{2b+a=-12-1=-13}}}
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{{{a=-3}}}
{{{b=-2}}}
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{{{highlight_green(2w^2-7w+6=(2w-3)(w-2))}}}