How do you factor $42 x^{2} + 35 x + 7$ $42x^2+35x+7$ ?

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How do you factor $42 x^{2} + 35 x + 7$ $42x^2+35x+7$ ?

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Answer 1 · 2018-06-17T07:59:50

$42 \cdot (x + \frac{1}{3}) (x + \frac{1}{2})$ $42*(x+1/3)(x+1/2)$

Explanation:

We solve the equation
$42 x^{2} + 35 x + 7 = 0$ $42x^2+35x+7=0$
dividing by $42$ $42$

$x^{2} + \frac{5}{6} x + \frac{1}{6} = 0$ $x^2+5/6x+1/6=0$
by the quadratic Formula we get

$x_{1, 2} = - \frac{5}{12} \pm \sqrt{\frac{25}{144} - \frac{24}{144}}$ $x_(1,2)=-5/12pmsqrt(25/144-24/144)$
so we get

$x_{1} = - \frac{1}{3}$ $x_1=-1/3$ or $x_{2} = - \frac{1}{2}$ $x_2=-1/2$

Answer 2 · 2018-06-17T08:56:23

#7(2x+1)(3x+1)

Explanation:

$take out a common factor 7$ $"take out a "color(blue)"common factor "7$

$= 7 (6 x^{2} + 5 x + 1)$ $=7(6x^2+5x+1)$

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

$the factors of the product 6 \times 1 = 6$ $"the factors of the product "6xx1=6$

$which sum to + 5 are + 3 and + 2$ $"which sum to + 5 are + 3 and + 2"$

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

$6 x^{2} + 3 x + 2 x + 1 \leftarrow factor by grouping$ $6x^2+3x+2x+1larrcolor(blue)"factor by grouping"$

$= 3 x (2 x + 1) + 1 (2 x + 1)$ $=color(red)(3x)(2x+1)color(red)(+1)(2x+1)$

$take out the common factor (2 x + 1)$ $"take out the "color(blue)"common factor "(2x+1)$

$= (2 x + 1) (3 x + 1)$ $=(2x+1)(color(red)(3x+1))$

$42 x^{2} + 35 x + 7 = 7 (2 x + 1) (3 x + 1)$ $42x^2+35x+7=7(2x+1)(3x+1)$

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How do you factor $42 x^{2} + 35 x + 7$ $42x^2+35x+7$ ?

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How do you factor 42x^2+35x+742x2+35x+742x^2+35x+7?

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How do you factor $42 x^{2} + 35 x + 7$ $42x^2+35x+7$ ?