Exercise 6 Page 49

To solve the given equation, we will start by factoring the left-hand side.

Factoring

Since the leading coefficient is 1, we need to rewrite - 3n as the sum of two terms whose coefficients have a product of 2. - 1 +(- 2)&= - 3 - 1(- 2)&= 2 Since - 1 and - 2 are two numbers whose sum is - 3 and whose product is 2, we will rewrite - 3n as - 1n+(- 2)n. Note that this expression can be simplified. - 1n+(- 2)n ⇔ - n-2n Therefore, we will start by rewriting - 3n as - n-2n.

Solving

To solve this equation, we will apply the Zero Product Property.

Checking the Answer

We can substitute our solutions back into the given equation and simplify to check if our answers are correct. We will start with n=1.

Substituting and simplifying created a true statement, so we know that n=1 is a solution to the equation. Let's move on to n=2.

Again, we obtained a true statement. Therefore, n=2 is indeed a solution to the equation.