Answer to Question #6239 in Algebra for Justin

Question

2
5a + 13a + 8

factor completely

Answer 1

Let's factor the expression by separating the complete square:
5a^2+13a+8=5(a^2+2a+1)+3a+3=5(a+1)^2+3(a+1)=(a+1)(5(a+1)+3)=(a+1)(5a+5+3)=(a+1)(5a+8)
Also we can do it in another way by finding roots of the given polynome:
5a^2+13a+8=0
D=13^2-4*8*5=169-160=9
a1=(-13+3)/10=-1
a2=(-13-3)/10=-16/10
Now we can factor the polynome as following:
5a^2+13a+8=5(a+1)(a+16/10)=(a+1)(5a+8) - no surprises, we've obtained the same result

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