Question

10:28:25, 2:49 pm
math 1215 final exam

1. complete the square in the expression. then factor the perfect square trinomial.

$x^2 + 6x$
complete the square
\boxed{} (do not factor.)
factor the result.
\boxed{}

Explanation:

Step1: Identify the coefficient of x

For the expression \(x^2 + 6x\), the coefficient of \(x\) is \(6\).

Step2: Take half of the coefficient of x

Half of \(6\) is \(\frac{6}{2}=3\).

Step3: Square the result

Squaring \(3\) gives \(3^2 = 9\).

Step4: Add and subtract (or just add in this case) the squared term to complete the square

To complete the square for \(x^2 + 6x\), we add \(9\) (since we don't need to subtract as we are just completing the square for the expression). So the expression becomes \(x^2 + 6x + 9\).

Step5: Factor the perfect square trinomial

A perfect square trinomial of the form \(a^2 + 2ab + b^2=(a + b)^2\). Here, \(a = x\) and \(b = 3\) (since \(2ab=2\times x\times3 = 6x\) and \(b^2 = 9\)), so \(x^2 + 6x + 9=(x + 3)^2\).

Answer:

Complete the square: \(x^2 + 6x + 9\)
Factor the result: \((x + 3)^2\)