How do you factor $3 x^{3} + x^{2} - 75 x - 25$ $3x^3+x^2-75x-25$ ?

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How do you factor $3 x^{3} + x^{2} - 75 x - 25$ $3x^3+x^2-75x-25$ ?

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Answer 1 · 2017-03-29T12:10:21

This actually requires factoring by grouping. Let's group the function like this: $(3 x^{3} + x^{2}) - (75 x + 25)$ $(3x^3+x^2)-(75x+25)$ . We then factor the two groups to get $x^{2} (3 x + 1) - 25 (3 x + 1)$ $x^2(3x+1)-25(3x+1)$ . The common factor between the two groups is $(3 x + 1)$ $(3x+1)$ , which we factor out to get $(3 x + 1) (x^{2} - 25)$ $(3x+1)(x^2-25)$ .

Now, we notice that $x^{2} - 25 = (x + 5) (x - 5)$ $x^2-25=(x+5)(x-5)$ (using the difference between squares identity).

Thus, our final answer is $(3 x + 1) (x + 5) (x - 5)$ $(3x+1)(x+5)(x-5)$

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How do you factor $3 x^{3} + x^{2} - 75 x - 25$ $3x^3+x^2-75x-25$ ?

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How do you factor $3 x^{3} + x^{2} - 75 x - 25$ $3x^3+x^2-75x-25$ ?