How do you factor $2 n^{2} - 7 n + 3$ $2n^2 - 7n + 3$ ?

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How do you factor $2 n^{2} - 7 n + 3$ $2n^2 - 7n + 3$ ?

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Answer 1 · 2016-05-18T10:05:19

$(2 x - 1) (x - 3)$ $(2x-1)(x-3)$

Explanation:

The general equation that factors as $(a x + b) (c x + d)$ $(ax+b)(cx+d)$ multiplies out to be $a c x^{2} + (a d + b c) x + b d$ $acx^2+(ad+bc)x+bd$ . This shows that the coefficient of the middle term is made up from factors of the coefficients of the outer terms.

Thus is this case we need factors of $2$ $2$ and $(- 3)$ $(-3)$ that will add (or subtract) to give $- 7$ $-7$ .

The only possible factors are $2$ $2$ and $1$ $1$ , and $3$ $3$ and $1$ $1$ .

The result is therefore $(2 x - 1) (x - 3)$ $(2x-1)(x-3)$

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How do you factor $2 n^{2} - 7 n + 3$ $2n^2 - 7n + 3$ ?

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