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

2 Answers
AltairSafir
Apr 17, 2018

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.

Elias
Apr 17, 2018

(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)

Related questions
See all questions in Factoring by Grouping
Impact of this question
4027 views around the world
You can reuse this answer
Creative Commons License