Math Problem Statement
how to do simple trinomials x^2 + 3x −18
Solution
To solve a simple trinomial such as , you typically factorize it into the form , where and are numbers that satisfy the following:
- Their sum is equal to the coefficient of , which is in this case.
- Their product is equal to the constant term, which is .
Steps:
-
Write down the equation:
-
Identify the sum and product conditions:
- (sum condition)
- (product condition)
-
Find two numbers that satisfy these conditions:
- The numbers and satisfy both conditions:
- The numbers and satisfy both conditions:
-
Write the factorized form:
-
(Optional) Verify by expanding:
Solution:
The factorized form of is:
If solving , the solutions are:
Would you like more examples or further clarification? Here are some related questions:
- How do you factor trinomials where the coefficient of is greater than 1?
- What is the difference between factoring and completing the square?
- How can trinomials be solved if they are not easily factorable?
- What are some tips for finding and quickly?
- How does this method relate to solving quadratic equations using the quadratic formula?
Tip: Always double-check your factorization by expanding it back to confirm the original expression.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring Trinomials
Quadratic Equations
Formulas
Factored form of a trinomial: (x + p)(x + q)
Sum and product conditions for factoring
Theorems
Zero Product Property
Suitable Grade Level
Grades 8-10