Question

Find the quotient when x2 + 10x + 21 is divided by x + 7

Answer 1

The quotient is
`x+3`

Explanation:

We first use the remainder theorem to determine whether
`x+7` is divisible by

`x^2+10x+21`:

`(-7)^2+10(-7)+21\\ = 49 - 70+21 = 0`

the remainder is zero which means
`x^2+10x+21` is divisible by
`x+7`.

Now, we could do polynomial long division to find the quotient, but in this case, it turns out that guessing is easier.

`x^2+10x+21`

is factored as

`x^2+10x+21 = (x+7)(x+3)`

which means

`(x^2+10x+21)/(x+7) =(x+3)`

which means the quotient is
`x+3.`