Answer:
The other binomial factor is (a+2).
Step-by-step explanation:
We have the expression [tex]a^2+7a+10[/tex], and we want to know the factors of this polynomial, then we have to factor the expression.
We can rewrite the expression:
[tex]a^2+7a+10=a^2+2a+5a+10[/tex]
Now we have a polynomial of four terms, then we can use grouping.
[tex](a^2+2a)+(5a+10)[/tex]
Part a:
[tex](a^2+2a)[/tex]
[tex](a^2+2a)=(a.a)+2.a[/tex]
We can see that both terms has [tex]a[/tex] in common, then we can apply common factor [tex]a[/tex],
[tex](a^2+2a)=a(a+2)[/tex]
Part b:
[tex](5a+10)[/tex]
[tex](5a+10)=5a+(2.5)[/tex]
Both terms has 5 in common, then we can apply common factor 5,
[tex](5a+10)=5(a+2)[/tex]
Now, going back to the expression:
[tex](a^2+2a)+(5a+10)=a(a+2)+5(a+2)[/tex]
Then, factoring by grouping:
[tex]a(a+2)+5(a+2)=(a+5)(a+2)[/tex]
We obtain the binomial factor (a+5) and the other binomial factor is (a+2)
