Question

What is (4x ^ 2 + 14x + 6) ÷ (x+3)

Answer 1

Hello!

We have the expression:

`(4x^2+14x+6)/(x+3)`

Note that all numbers in the numerator are even. So, we can put 2 in evidence, look:

`(2(2x^2+7x+3))/(x+3)`

Now, let's rewrite 7x as 6x+x:

`(2(2x^2+6x+x+3))/(x+3)`

The first and second terms are multiples of 2x, so let's rewrite it putting it in evidence too:

`(2(2x(x+3)+x+3))/(x+3)`

Another term appears twice: (x+3). So, we'll have:

`(2(x+3)(2x+1))/(x+3)`

Canceling the common factors:

`\frac{2\cancel{x+3}(2x+1)}{\cancel{x+3}}=2(2x+1)=\boxed{4x+2}`

Answer:

4x +2.