Question

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

Explanation:

Step1: Factor the numerator

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

Step2: Cancel common factors

Cancel the common factor \((x + 7)\) from the numerator and the denominator (assuming \(x
eq - 7\)). We are left with \(\frac{x + 3}{4}\).

Answer:

\(\frac{x + 3}{4}\) (which corresponds to the option \(\frac{x+3}{4}\))