Question

When factoring a trinomial using the diamond method, you find 2 terms that multiply to the top term and add to the bottom term (DONT ANSWER IF YOU DONT KNOW WHAT IM TALKING ABOUT.) If needed, how do you know which term gets the negative sign if you need to subtract the 2 terms to get the needed sum and/or the number your multiplying to is negative?

Answer 1

When using the diamond method to factor a trinomial, if the two terms that multiply to the top term and add to the bottom term have opposite signs, the larger term will have the same sign as the middle term of the trinomial, and the smaller term will have the opposite sign.

For example, let's say we want to factor the trinomial x^2 - 6x - 7. We can use the diamond method to find two numbers that multiply to -7 and add to -6:

-7 can be factored as -1 x 7 or 1 x -7

-1 + 7 = 6, so -1 and 7 are the two numbers that add up to -6.

To factor the trinomial, we rewrite the middle term (-6x) as the sum of these two terms: -x + 7x. This gives us:

x^2 - x + 7x - 7

Now we group the first two terms and the last two terms:

x(x - 1) + 7(x - 1)

Notice that we have a common factor of (x - 1), so we can factor it out:

(x - 1)(x + 7)

So the factored form of the trinomial x^2 - 6x - 7 is (x - 1)(x + 7).

In this case, we see that the larger term (7) has the same sign as the middle term (-6x) of the trinomial, while the smaller term (-1) has the opposite sign. This is because -7 is negative, so to get a negative sum, we need to subtract the smaller term (-1) from the larger term (7).

Answer 2

I had a question like this one time. When you have your polynomial equation, you do the diamond method, right? You then choose whichever answer matches the equation. So let's say it's between -1 and 7 or -7 and 1 to get -6x. You would add/subtract the two side numbers and whichever makes sense, you would put them in the equation.