How do you factor #y=x^2 - 2x - 15#

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Question

How do you factor #y=x^2 - 2x - 15#

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Eva Adamson · Accepted Answer

#y=(x-5)(x+3)# #"the factors of - 15 which sum to - 2 are - 5 and + 3"# #y=(x-5)(x+3)#

Ethan Adkins · Answer

#(x-5)(x+3)# First, find two numbers that have a sum of -2 (the second term) and have a product of -15 (the third term) Multiples of 15: 1 | 15 3 | 5 #-5 * 3 = -15# and #-5 + 3 = -2# Use this to "split the middle" of the polynomial #x^2 - 5x + 3x - 15# Factor #x(x-5) + 3(x-5)# #(x-5)(x+3)#

Savannah Anderson · Answer

undefined To factor $ y = x^2 - 2x - 15 $, we first look for two numbers that multiply to -15 (the constant term) and add up to -2 (the coefficient of the linear term). These numbers are -5 and 3.

Then, we can rewrite the middle term (-2x) as the sum of these two numbers:
$ y = x^2 - 5x + 3x - 15 $.

Next, we group the terms and factor by grouping:
$ y = (x^2 - 5x) + (3x - 15) $.
$ y = x(x - 5) + 3(x - 5) $.

Now, we factor out the common factor of $ x - 5 $:
$ y = (x + 3)(x - 5) $.

So, the factored form of $ y = x^2 - 2x - 15 $ is $ y = (x + 3)(x - 5) $.