Question

If you’re using the inspection method, what constant term would you need in the numerator of this rational expression for (x+5) to be a common factor? (x^2+6x+14) / (x+5)

Answer 1

Answer with explanation:

We want , (x+5) to be a Common factor of the rational expression

     $=\frac{x^2+6 x+14}{x+5}$

So, if we write

 x^2+6 x+14=x²+6 x+ 5+9

So, to get (x+5) as a common factor, we should subtract 9 from the Quadratic expression.

    $\Rightarrow \frac{x^2+6 x+14-9}{x+5}\\\\=\frac{x^2+6 x+5}{x+5}\\\\=\frac{x^2+5 x+x+5}{x+5}\\\\=\frac{x \times (x+5)+1 \times (x+5)}{x+5}\\\\=\frac{(x+5)(x+1)}{x+5}\\\\=x+1$

⇒Subtract ,9 from the Numerator,That is constant term that we need in Numerator = -9

Answer 2

If I am using the inspection method, the constant term that I would need in the numerator of this rational expression for (x+5) to be a common factor of (x^2+6x+14) / (x+5) is 11/(x+1)