How do you factor $3 b^{2} - 48 b + 189$ $3b ^ { 2} - 48b + 189$ ?

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How do you factor $3 b^{2} - 48 b + 189$ $3b ^ { 2} - 48b + 189$ ?

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Answer 1 · 2018-02-15T10:03:21

$3 b^{2} - 48 b + 189$ $3b^2−48b+189$
taking 3 as a common factor.,

$3 (b^{2} - 16 b + 63)$ $3(b^2−16b+63 )$
$3 (b^{2} - 7 b - 9 b + 63)$ $3(b^2−7b-9b+63 )$
$3 (b (b - 7) - 9 (b - 7))$ $3(b(b−7)-9(b-7))$
$3 (b - 9) (b - 7)$ $3(b−9)(b-7)$

Answer 2 · 2018-02-15T10:14:48

$3 (b - 9) (b - 7)$ $3(b-9)(b-7)$

Explanation:

$take out a common factor of 3$ $"take out a "color(blue)"common factor of 3"$

$\Rightarrow 3 (b^{2} - 16 b + 63) \leftarrow factor the quadratic$ $rArr3(b^2-16b+63)larrcolor(blue)"factor the quadratic"$

$the factors of + 63 which sum to - 16 are - 9 and - 7$ $"the factors of + 63 which sum to - 16 are - 9 and - 7"$

$\Rightarrow 3 (b - 9) (b - 7)$ $rArr3(b-9)(b-7)$

$\Rightarrow 3 b^{2} - 48 b + 189 = 3 (b - 9) (b - 7)$ $rArr3b^2-48b+189=3(b-9)(b-7)$

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How do you factor $3 b^{2} - 48 b + 189$ $3b ^ { 2} - 48b + 189$ ?

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