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How do you use factors by grouping?

How do you use factors by grouping?-example-1

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140x^3+105x^2-40x-30\implies (140x^3+105x^2)+(-40x-30) \\\\\\ (140x^3+105x^2)-(40x+30) \implies 35x^2(4x+3)-(40x+30) \\\\\\ \stackrel{\textit{common factoring}}{35x^2(4x+3)-10(4x+3)}\implies \stackrel{\textit{common factoring}}{(4x+3) ~ ~~ ~ (35x^2-10)}

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