3x^2 - 15x + 18
(x-18)(x+3)
(x-9)(x-6) is the correct answer not the previous answer
To factor the quadratic expression 3x^2 - 15x + 18, we can follow these steps:
Step 1: Check for common factors
First, we look for any common factors among the coefficients (numbers) of the quadratic expression. In this case, all coefficients are divisible by 3, so we can factor out the common factor 3:
3(x^2 - 5x + 6)
Step 2: Factor the quadratic trinomial
Next, we focus on factoring the quadratic trinomial x^2 - 5x + 6. We need to find two binomials whose product gives us this trinomial. To do this, we can look for two numbers that multiply to give the constant term (6) and add up to give the coefficient of the linear term (-5).
In this case, the numbers that fit these criteria are -3 and -2. We can rewrite the trinomial as follows:
3(x^2 - 3x - 2x + 6)
Step 3: Group the terms
Now, we group the terms in pairs by adding parentheses:
3[(x^2 - 3x) + (-2x + 6)]
Step 4: Factor by grouping
Within each pair of grouped terms, we can factor out the greatest common factor. From the first pair, we factor out an x:
3[x(x - 3) + (-2x + 6)]
From the second pair, we factor out -2:
3[x(x - 3) - 2(x - 3)]
Now, we see that we have a common binomial factor, (x - 3), which we can factor out:
3(x - 3)(x - 2)
So, the factored form of the quadratic expression 3x^2 - 15x + 18 is 3(x - 3)(x - 2).