Question 850615
{{{-5t^2+40t-35}}}


{{{-5(t^2-8t+7)}}}


{{{-5(t^2-t-7t+7)}}} See <font color="red">Special Note</font> below


{{{-5((t^2-t)+(-7t+7))}}}


{{{-5(t(t-1)+(-7t+7))}}}


{{{-5(t(t-1)-7(t-1))}}}


{{{-5(t-7)(t-1)}}}



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{{{-5t^2+40t-35}}} completely factors to {{{-5(t-7)(t-1)}}}


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<font color="red">Special Note</font>: You need to find two numbers that multiply to 7 (last term in {{{t^2-8t+7}}}) and that also add to -8 (middle coefficient in {{{t^2-8t+7}}}). These two numbers are -1 and -7. So that's why {{{-8t}}} breaks up into {{{-t-7t}}}. From there, we factor by grouping.