How do you factor $7 c^{2} - 16 c + 9$ $7c^2-16c+9$ ?

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How do you factor $7 c^{2} - 16 c + 9$ $7c^2-16c+9$ ?

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Answer 1 · 2016-05-02T21:12:55

$7 c^{2} - 16 c + 9 = (7 c - 9) (c - 1)$ $7c^2-16c+9= (7c-9)(c-1)$

Explanation:

Notice that $16 = 7 + 9$ $16 = 7+9$ . So the middle term splits to give us an easy factoring by grouping:

$7 c^{2} - 16 c + 9$ $7c^2-16c+9$

$= 7 c^{2} - 7 c - 9 c + 9$ $= 7c^2-7c-9c+9$

$= (7 c^{2} - 7 c) - (9 c - 9)$ $= (7c^2-7c)-(9c-9)$

$= 7 c (c - 1) - 9 (c - 1)$ $= 7c(c-1)-9(c-1)$

$= (7 c - 9) (c - 1)$ $= (7c-9)(c-1)$

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