How do you factor $3 x^{2} - 4 x + 1$ $3x^2 -4x +1$ ?

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How do you factor $3 x^{2} - 4 x + 1$ $3x^2 -4x +1$ ?

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Answer 1 · 2018-05-25T08:55:10

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

Explanation:

$using the a-c method to factor the quadratic$ $"using the a-c method to factor the quadratic"$

$the factors of the product 3 \times 1 = 3$ $"the factors of the product "3xx1=3$

$which sum to - 4 are - 3 and - 1$ $"which sum to - 4 are - 3 and - 1"$

$split the middle term using these factors$ $"split the middle term using these factors"$

$3 x^{2} - 3 x - x + 1 \leftarrow factor by grouping$ $3x^2-3x-x+1larrcolor(blue)"factor by grouping"$

$= 3 x (x - 1) - 1 (x - 1)$ $=color(red)(3x)(x-1)color(red)(-1)(x-1)$

$take out the common factor (x - 1)$ $"take out the "color(blue)"common factor "(x-1)$

$= (x - 1) (3 x - 1)$ $=(x-1)(color(red)(3x-1))$

$3 x^{2} - 4 x + 1 = (x - 1) (3 x - 1)$ $3x^2-4x+1=(x-1)(3x-1)$

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How do you factor $3 x^{2} - 4 x + 1$ $3x^2 -4x +1$ ?

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