Question

How do you factor `14x^2+23xy+3y^2`?

Answer 1

`(2x+3y)(7x+y)`

Explanation:

`"although the quadratic has 2 variables we deal with it"`
`"in the same manner as one variable quadratics"`

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

`"the factors of the product "14xx3=42`

`"which sum to + 23 are + 21 and + 2"`

`"split the middle term using these factors"`

`14x^2+21xy+2xy+3y^2larrcolor(blue)"factor by grouping"`

`=color(red)(7x)(2x+3y)color(red)(+y)(2x+3y)`

`"take out the "color(blue)"common factor "(2x+3y)`

`=(2x+3y)(color(red)(7x+y))`

`14x^2+23xy+3y^2=(2x+3y)(7x+y)`