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How do you factor #x^2+4x+4#?

Answer 1

Factoring by #color(blue)(GROUPING)# :

#x^2 + 4x+ 4# in general form is #ax^2 + bx + c# :

here: #color(red)(a)# #=# 1 (coefficient of #x^2#) #color(red)(b)# #=# 4(coefficient of #x#) #color(red)(c)# #=# 4 (constant term)

now: a #.# c #=# 4 (product of first and last term of the equation)

now, we need to find two factors of #a.c# which need to add up to the middle term (which is b )

#a.c = 4.1 # #a.c = 2.2# , here , 2+2 adds up to 4:

so we can factor as follows: #x^2 + 4x+ 4 = x^2 + 2x + 2x + 4# (splitting middle term)

# = x(x+2) + 2(x +2)# ( taking out common terms ) #= (x+2)(x+2)#

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Answer 2

Jameson Allen

To factor (x^2 + 4x + 4), you look for two numbers that multiply to give you the last term (4) and add to give you the middle term (4). In this case, those numbers are 2 and 2. So, the factored form is ((x + 2)(x + 2)), or simply ((x + 2)^2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.