Question 105099
{{{12b^3-86b^2+14b=2b(6b^2-43b+7)}}}

To factor {{{6b^2-43b+7}}}, first, read my lesson entitled,"Factoring trinomials: SHORTCUT!!!" then go back to this page.

By the quadratic formula,

{{{b=(43+-sqrt(43^2-4*6*7))/(2*6)}}}
{{{b=(43+-sqrt(1849-168))/(12)}}}
{{{b=(43+sqrt(1681))/(12)}}} or {{{b=(43-sqrt(1681))/(12)}}}
{{{b=(43+41)/(12)}}} or {{{b=(43-41)/(12)}}}
{{{b=84/12}}} or {{{b=2/12}}}
{{{b=7}}} or {{{b=1/6}}}

If {{{b=7}}},
{{{b-7=0}}}
If {{{b=1/6}}},
{{{6b-1=0}}}

Thus,
{{{6b^2-43b+7=(b-7)(6b-1)}}} 

And therefore,
{{{12b^3-86b^2+14b=2b(b-7)(6b-1)}}}


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HyperBrain!