Question

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

Answer 1

Answer:

The quotient is $x+3$

Step-by-step 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

$\dfrac{x^2+10x+21}{x+7} =(x+3)$

which means the quotient is $x+3.$