How do you simplify #(p²-3p-28) /( p²-4p-21)#?

1 Answer
Don't Memorise
Oct 23, 2015

#(p²-3p-28) /( p²-4p-21) = color(green)((p+4)/(p+3)#

Explanation:

Let's look at the 2 polynomials separately

#color(red)(p²-3p-28#
# = p^2 -7p +4p - 28#
# = p(p-7) + 4(p - 7)#
# = (p-7)(p+4)#

#color(red)( p²-4p-21#
# = p^2 - 7p + 3p -21#
# = p(p-7) + 3(p-7)#
#=(p-7)(p+3)#

Hence #(p²-3p-28) /( p²-4p-21) = {cancel((p-7))(p+4)}/{cancel((p-7))(p+3)}#

# = color(green)((p+4)/(p+3)#

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