Question

Factor the expression. ×^2+7×+10

Answer 1

[AI-generated answer — Bot GPT 3.5]

The expression x^2 + 7x + 10 can be factored as (x + 2)(x + 5).

Answer 2

[AI-generated answer — Step-by-Step Bot]

To factor the expression x^2 + 7x + 10, follow these steps:

Step 1: Write down two sets of parentheses: ( )( ).

Step 2: Determine what two numbers will multiply to give you 10 and add up to give you 7. In this case, the numbers are 2 and 5 because 2 * 5 = 10 and 2 + 5 = 7.

Step 3: Place these two numbers into the parentheses, so you have (x + 2)(x + 5).

Therefore, the factored form of the expression x^2 + 7x + 10 is (x + 2)(x + 5).

Answer 3

[AI-generated answer — Explain Bot]

To factor the expression x^2 + 7x + 10, we need to find two binomial expressions such that when multiplied together, they result in the given expression. The pattern we're looking for is called "factoring by grouping".

First, we multiply the coefficient of the x^2 term (which is 1) with the constant term (which is 10). In this case, 1 * 10 = 10. We need to find two numbers that multiply to 10 and add up to the coefficient of the x term, which is 7.

So, let's list the factor pairs of 10:
1 * 10 = 10
2 * 5 = 10

Clearly, the pair 2 and 5 adds up to 7, which is what we need. Therefore, we can rewrite the expression as follows:

x^2 + 2x + 5x + 10

Now, we'll group the terms:

(x^2 + 2x) + (5x + 10)

Next, we factor out the greatest common factor from each group:

x(x + 2) + 5(x + 2)

Notice that within each pair of parentheses, we have the same expression, (x + 2). This means that (x + 2) is a common factor of both terms.

Therefore, we can write the factored form as:

(x + 2)(x + 5)

And there you have it! The factored form of the expression x^2 + 7x + 10 is (x + 2)(x + 5).