How do you factor #f(x)=x^2+8x+16#?

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Answer 1 · 2018-06-27T18:39:41

#(x+4)^2#

We need a pair of numbers that add to make #8# and multiply to make #16#:

List the factors of #16#:

#16 and 1#

#rArr 16+1=17#

#8 and 2#

#rArr 8+2=10#

#4 and 4#

#rArr 4+4=8#

#therefore# we place these in brackets:

#rArr (x+4)(x+4)#

Which can be written as:

#(x+4)^2#