Factoring trinomials; i’m a little confused on this question ; (

(x + 9)(n - 10)

Step-by-step explanation:

This trinomial is of the form

x^2 + ax + b

There is no number multiplying x^2.

To factor a trinomial of this type, set up two sets of parentheses:

(       )(       )

Place the variable inside each set of parentheses on the left side.

(x    )(x     )

Now look for two numbers that multiply to "b" and add to "a."

Place those two numbers inside the two sets of parentheses on the right side. Include + for a positive number and - for a negative number.

Let's work out your problem.

Factor n^2 - n - 90.

We see that there is no number multiplying the 2nd degree term since we have only n^2, not 2n^2 or 3n^2, etc.

We set up two sets of parentheses and place the variable n on the left side of each.

(n    )(n    )

Now we need two numbers that multiply to "b" and add to "a". Notice above, in x^2 + ax + b that b is the term that is just a number. "a" is the coefficient of the x-term. In your trinomial, n^2 - n - 90, a = -1 and b = -90. We need two numbers that multiply to -90 and add to -1. Since the two numbers must multiply to a negative number, -90, we must have a positive number and a negative number. 9 and -10 do multiply to -90. Also 9 and -10 add to -1. Now just place 9 and -1 in the parentheses on the right side. Include a "+" with the 9 and the negative sign with the 10.

(n + 9)(n - 10)