How do you factor #b^2+4b-60#?

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Answer 1 · 2015-05-02T05:08:24

We can split the middle term of this expression to factorise it

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*-60 = -60#
AND
#N_1 +N_2 = b = 4#

After trying out a few numbers we get #N_1 = 10# and #N_2 = - 6#

#10*-6 = 60#, and #10+(-6) = 4#

#b^2+4b-60 = b^2 + 10b - 6b - 60#

# = b(b+10) - 6(b+10)#

#b + 10# is a common factor to each of the terms

# =color(green)( (b+10)(b-6)#