How do you factor the trinomial $x^{2} - 12 x + 35$ $x^2-12x+35$ ?

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How do you factor the trinomial $x^{2} - 12 x + 35$ $x^2-12x+35$ ?

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Answer 1 · 2018-03-15T16:15:08

See a solution process below:

Explanation:

Because the $x^{2}$ $x^2$ coefficient is $1$ $1$ we know the coefficient for the $x$ $x$ terms in the factor will also be $1$ $1$ :

$(x) (x)$ $(x )(x )$

Because the constant is a positive and the coefficient for the $x$ $x$ term is a negative we know the sign for the constants in the factors will both be negative because a negative plus a negative is a negative and negative times a negative is a positive:

$(x -) (x -)$ $(x - )(x - )$

Now we need to determine the factors which multiply to 35 and also add to 12:

$1 \times 35 = 35$ $1 xx 35 = 35$ ; $1 + 35 = 36$ $1 + 35 = 36$ <- this is not the factor

$5 \times 7 = 35$ $5 xx 7 = 35$ ; $5 + 7 = 12$ $5 + 7 = 12$ <- this IS the factor

$(x - 5) (x - 7)$ $(x - 5)(x - 7)$

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How do you factor the trinomial $x^{2} - 12 x + 35$ $x^2-12x+35$ ?

1 Answer

Explanation:

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