How do you factor the trinomial $x^2 + 7x + 10$ ?

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Answer 1 · 2016-03-05T21:47:24

$(x+5)(x+2)$

Open two sets of brackets. Factors of $x^2$ are $x, x$ . Since the expressions are positive, both signs will be positive.
$(x+?)(x+?)$

Multiply the first and last coefficients. +1 x +10 = +10.
The factors of +10 are: +1, +10; +2, +5; -2,-5; and -1, -10. Add each.

The second one adds to +7, the middle coefficient. So, +2, and +5 are correct.

$(x+5)(x+2)$

How do you factor the trinomial x^2 + 7x + 10x^2 + 7x + 10?