Question

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

Answer 1

`42*(x+1/3)(x+1/2)`

Explanation:

We solve the equation
`42x^2+35x+7=0`
dividing by `42`

`x^2+5/6x+1/6=0`
by the quadratic Formula we get

`x_(1,2)=-5/12pmsqrt(25/144-24/144)`
so we get

`x_1=-1/3` or `x_2=-1/2`

Answer 2

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

Explanation:

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

`=7(6x^2+5x+1)`

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

`"the factors of the product "6xx1=6`

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

`"split the middle term using these factors"`

`6x^2+3x+2x+1larrcolor(blue)"factor by grouping"`

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

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

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

`42x^2+35x+7=7(2x+1)(3x+1)`