I have to come up with examples of how to factor a trinomial; factoring with
!=a and I have no idea what that even means. Can anyone explain or give me an example? It'd really be appreciated :)
Certainly! Factoring a trinomial with a leading coefficient that is not equal to 1 (denoted as "!=") involves finding two binomials that, when multiplied together, yield the given trinomial. Let me break down the process for you using an example:
Example Trinomial: 2x^2 + 7x + 3
Step 1: Multiply the leading coefficient (in this case, 2) by the constant term (in this case, 3), which gives you 2 * 3 = 6.
Step 2: Find two numbers whose sum is equal to the coefficient of the middle term (in this case, 7) and whose product is equal to the result obtained in Step 1 (in this case, 6). In this example, the numbers are 2 and 3, since 2 + 3 = 5 and 2 * 3 = 6.
Step 3: Rewrite the original trinomial as the sum of the numbers obtained in Step 2, but using those numbers as coefficients for the x-term. This will give you: 2x^2 + 2x + 3x + 3.
Step 4: Group the terms in pairs and factor out the greatest common factor from each pair. In this example, you can factor out 2 from the first two terms and 3 from the last two terms. This yields: 2x(x + 1) + 3(x + 1).
Step 5: Notice that both pairs have a common factor, (x + 1). Factor out this common binomial to obtain the final factored form: (x + 1)(2x + 3).
So, the factored form of the trinomial 2x^2 + 7x + 3 is (x + 1)(2x + 3).
Remember, practicing with more examples will help you become more comfortable with factoring trinomials with a leading coefficient not equal to 1.