Question

How do you factor by grouping `x^2 + 7x + 5x + 35`?

Answer 1

`x^2+(7+5)*x+35=(x+5)(x+7)`

Explanation:

`x^2+(7+5)*x+35=`
`=x^2+(7+5)*x+(5*7)=`
`=(x+5)(x+7)`

Remember:
`x^2+(a+b)*x+a*b=(x+a)(x+b)`
For more click here. If you are interested in general polynomial: Vieta's formulas.

Answer 2

`(x+7)(x+5)`

Explanation:

Grouping is a technique usually used when there is no factor common to all terms of a polynomial, but there are factors common to some of the terms, so I am not sure if this is the correct technique to answer this question.
Before we solve this problem, let me show you the FOIL method.
(x+a)(x+b)
Begin by multiplying the First terms (`x*x`), then the Outer terms
(`x*b`), Inner terms (`a*x`), and finnally Last terms (`a*b`)
If we right that all out then we would have the equation
`x^2+ax+bx+ab` Now we apply this to your question..
`x^2 +7x+5x+35`
Matching these equations side by side it is clear that `a=7 and b=5`
When they are asking you to (group them) I assume that they are asking you to return them to the original format `(x+a)(x+b)`
Simply plug in 7 and 5 for "a" and "b" and you get your answer...
`(x+7)(x+5)`