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

Answer 1

Abigail Allen

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

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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Answer 2

Ethan Adkins

To simplify the expression (p²-3p-28) /( p²-4p-21), you can factor both the numerator and denominator. The numerator factors to (p-7)(p+4), and the denominator factors to (p-7)(p+3). Cancel out the common factor of (p-7) from both the numerator and denominator. The simplified expression is (p+4)/(p+3).

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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.