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

Question

Eva Abramson · Accepted Answer

#x^2+(7+5)*x+35=(x+5)(x+7)# #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.

Avery Alexander · Answer

#(x+7)(x+5)# 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)#

Savannah Anderson · Answer

undefined To factor by grouping x^2 + 7x + 5x + 35, you group the first two terms together and the last two terms together: (x^2 + 7x) + (5x + 35). Then, you factor out the greatest common factor from each group: x(x + 7) + 5(x + 7). Finally, you factor out the common binomial factor, which is (x + 7), to get the final factored expression: (x + 7)(x + 5).