Simplify completely quantity x squared plus 12 x plus 35 all over 3 x plus 15.

Solution:

Given, quantity x squared plus 12 x plus 35 all over 3 x plus 15.

The expression can be written as \(\frac{x^{2}+12x+35}{3x+15}\)

Converting the numerator in factored form,

\(x^{2}+12x+35\) = \(x^{2}+7x+5x+35\)

= \(x(x+7)+5(x+7)\)

= \((x+7)(x+7)\)

Rewriting the term in denominator by taking out 3,

3x + 15 = 3(x + 5)

Now, the equation becomes

\(\frac{x^{2}+12x+35}{3x+15}\) = \(\frac{(x+7)(x+5)}{3(x+5)}\)

= \(\frac{(x+7)}{3}\)

Therefore, the simplified form is \(\frac{(x+7)}{3}\)

Simplify completely quantity x squared plus 12 x plus 35 all over 3 x plus 15.

Summary:

The completely simplified form of quantity x squared plus 12 x plus 35 all over 3 x plus 15 is \(\frac{(x+7)}{3}\)