How do you factor the expression #x^2 + 5x + 4#?

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Answer 1 · 2016-04-26T21:15:26

#x^2+5x+4 = (x+4)(x+1)#

Find a pair of factors of #4# with sum #5#.

The pair #4, 1# works.

Hence:

#x^2+5x+4 = (x+4)(x+1)#

In general note that:

#(x+a)(x+b) = x^2+(a+b)x+ab#

So if you are given a polynomial to factor in the form:

#x^2+px+q#

then you can try finding a pair of factors of #q# with sum #p#.

If you can find #a, b# such that #a+b = p# and #ab = q#, then:

#x^2+px+q = (x+a)(x+b)#