Problem 17
Question
Factor each trinomial, or state that the trinomial is prime. $$x^{2}+5 x+6$$
Step-by-Step Solution
Verified Answer
So, the factored form of the trinomial \(x^{2}+5x+6\) is \( (x+2)(x+3)\).
1Step 1: Identify the structure
Recognize that the given expression is a quadratic trinomial in the form \(ax^2 + bx + c\), where \(a=1\), \(b=5\), and \(c=6\).
2Step 2: Find factors
Search for two numbers that multiply to 6 (the value of \(c\)) and add up to 5 (the value of \(b\)). The numbers 2 and 3 fit these criteria because \(2*3 = 6\) and \(2+3 = 5\).
3Step 3: Write the factors
Write the trinomial as a product of two binomials using the identified numbers as the coefficients of \(x\) in the binomials, giving \( (x+2)(x+3) \).
Other exercises in this chapter
Problem 16
Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{2 x+y}{x y-2 x}, \text { for } x=-2 \text { and } y=4$$
View solution Problem 17
multiply or divide as indicated. $$ \frac{x^{2}-9}{x^{2}} \cdot \frac{x^{2}-3 x}{x^{2}+x-12} $$
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In Exercises 15–58, find each product. $$ (2 x-3)\left(x^{2}-3 x+5\right) $$
View solution Problem 17
Use the product rule to simplify the expressions in Exercises \(13-22 .\) In Exercises \(17-22,\) assume that variables represent nonnegative real numbers. $$ \
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