a2-10a+24=

Question

can you walk me though this having trouble understanding it

 

Answer 1

a²-10a+24=0

 

To factor, you want two binomials such that:

 

(a+m)(a+n) = a²-10a+24=0

 

If we multiply the binomials out using the FOIL method, we get:

 

a² + na + ma + mn = a² -10a + 24 = 0

a² + (n+m)a + mn = a² -10a + 24 = 0

 

So to figure out what m and n are, we need two numbers that multiply to give 24 (=mn) and add to give -10 (=m+n).  Some possibilities are ±12 and ±2, ±8 and ±3, ±6 and ±4.  Let's try m=-6 and n=-4:

 

mn = (-6)(-4) = +24

 

m+n = (-6) + (-4) = -10

 

This solution works, so the answer is:

 

(a-6)(a-4) = 0

 

a = 6 and 4