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Can You Solve This Easy Algebra Riddle?
Are you ready to put your algebra skills to the test? This riddle is designed to challenge your thinking and help you practice your knowledge of trinomials. So, grab a pencil and paper, and let's see if you can crack the code!
The Riddle:
I am a trinomial, with three terms in my expression.
My first term is x2, and my last term is 9.
My middle term is a number that makes me factorable into two binomials.
What is the middle term of this trinomial?
Solution:
To find the middle term, we need to think about how trinomials are factored. A trinomial is factorable if it can be expressed as the product of two binomials.
Let's break down the problem:
- The first term is x2, which means each binomial must start with 'x'.
- The last term is 9, which means the last terms of the binomials must multiply to 9.
Now, we need to find the factors of 9 that, when added together, will give us the middle term of the trinomial. The factors of 9 are 1, 3, and 9. Let's try different combinations:
| Binomial 1 | Binomial 2 | Middle Term |
|---|---|---|
| (x + 1) | (x + 9) | 10x |
| (x + 3) | (x + 3) | 6x |
| (x - 1) | (x - 9) | -10x |
| (x - 3) | (x - 3) | -6x |
The only combination that gives us a factorable trinomial is (x + 3)(x + 3). This means the middle term of the trinomial is 6x.
Therefore, the middle term of the trinomial is 6x.
This riddle is a great way to practice factoring trinomials and understanding the relationship between the coefficients of a trinomial and its factors. Keep practicing, and you'll become a master of algebra in no time!