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

2 Answers
Apr 17, 2018

Answer:

#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.

Apr 17, 2018

Answer:

#(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)#