I don't understand factoring. One of my homework questions asks for that. The question is "The area of a rectangular garden is given by the trinomial x to the 2nd power plus x -42. What are the possible dimensions of the rectangle? Use factoring.

why all the words?

a = x^2+x-42
Factor that to get
a = (x+7)(x-6)

Factoring is a strategy used in algebra to express a polynomial as a product of its factors. In this case, you are given the trinomial x² + x - 42 and asked to find the possible dimensions of the rectangle.

To factor a trinomial like this, you need to find two binomials such that when multiplied together, they yield the given trinomial. In other words, you have to break down the trinomial into its factors.

To begin factoring, you'll want to look for two numbers that multiply to give -42 and add up to the coefficient of the x-term, which is 1. You can do this by considering the factors of -42 and testing different combinations until you find the correct pair.

In this case, the factors of -42 are: -1, 1, -2, 2, -3, 3, -6, 6, -7, 7, -14, and 14.

By testing different combinations, you'll find that -6 and 7 are the numbers that satisfy the condition. Adding -6 and 7 gives you the coefficient of the x-term, which is 1.

Now that you have the correct pair of numbers, you can rewrite the trinomial as a product of two binomials:

x² - 6x + 7x - 42

Next, you group the terms:

(x² - 6x) + (7x - 42)

Now factor out common terms from each group:

x(x - 6) + 7(x - 6)

Notice that both terms have the common factor of (x - 6). Factor that out:

(x - 6)(x + 7)

Now you have factored the trinomial x² + x - 42 as (x - 6)(x + 7).

To find the possible dimensions of the rectangle, you can use the factored form. Since the area of a rectangle is length times width, the possible dimensions are the factors of the trinomial: (x - 6) and (x + 7).

Therefore, the possible dimensions of the rectangle are x - 6 and x + 7.