Question

The binomial (a+5) is a factor of a2+7a+10. What is the other factor?

Answer 1

The other binomial factor is (a+2).

Explanation:

We have the expression
`a^2+7a+10`, and we want to know the factors of this polynomial, then we have to factor the expression.

We can rewrite the expression:

`a^2+7a+10=a^2+2a+5a+10`

Now we have a polynomial of four terms, then we can use grouping.

`(a^2+2a)+(5a+10)`

Part a:

`(a^2+2a)`

`(a^2+2a)=(a.a)+2.a`

We can see that both terms has
`a` in common, then we can apply common factor
`a`,

`(a^2+2a)=a(a+2)`

Part b:

`(5a+10)`

`(5a+10)=5a+(2.5)`

Both terms has 5 in common, then we can apply common factor 5,

`(5a+10)=5(a+2)`

Now, going back to the expression:

`(a^2+2a)+(5a+10)=a(a+2)+5(a+2)`

Then, factoring by grouping:

`a(a+2)+5(a+2)=(a+5)(a+2)`

We obtain the binomial factor (a+5) and the other binomial factor is (a+2)