Question

question 6 (multiple choice worth 5 points) (04.01r mc) what is the simplified form of the expression \\(\frac{x^2 + 10x + 21}{4(x + 3)}\\)? \\(\frac{x - 7}{4}\\) \\(\frac{x + 7}{4}\\) \\(\frac{x + 7}{x + 3}\\) \\(\frac{x - 7}{x + 3}\\)

Explanation:

Step1: Factor the numerator

We factor the quadratic expression \(x^2 + 10x + 21\). We need two numbers that multiply to \(21\) and add up to \(10\). Those numbers are \(3\) and \(7\). So, \(x^2 + 10x + 21=(x + 3)(x + 7)\).
The expression becomes \(\frac{(x + 3)(x + 7)}{4(x + 3)}\).

Step2: Cancel common factors

We can cancel out the common factor \((x + 3)\) from the numerator and the denominator (assuming \(x
eq - 3\) to avoid division by zero). After canceling, we are left with \(\frac{x + 7}{4}\).

Answer:

\(\frac{x + 7}{4}\) (which corresponds to the option with \(\frac{x + 7}{4}\))