factoring polynomials

Question

x to the second power - 11xy + 24y to the second power

 

is it a prime

Answer 1

x² - 11x + 24

 

When factoring, you want two numbers that multiply to give 24 and add to give -11.  -8 and -3 fit the bill:

• (-8)*(-3) = 24
• (-8) + (-3) = -11

 

So x² - 11x + 24 = (x-8)(x-3).  Since it factors, it's not prime.