Question

what is the expression in factored form

x^2+13x+42

Answer 1

[AI-generated answer — Bot GPT 4]

The factored form of the expression x^2+13x+42 is (x+6)(x+7).

Answer 2

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

To find the expression in factored form, we need to factorize the quadratic equation x^2 + 13x + 42.

Step 1: Find two numbers that multiply to give the constant term (42) and add up to give the coefficient of the linear term (13). In this case, the numbers are 6 and 7 because 6*7 = 42 and 6 + 7 = 13.

Step 2: Rewrite the quadratic equation using the two numbers found in Step 1. We can replace the middle term (13x) with the sum of the two numbers. The equation becomes:
x^2 + 6x + 7x + 42

Step 3: Group the terms with common factors:
(x^2 + 6x) + (7x + 42)

Step 4: Factor out the greatest common factor from each group. In this case, the greatest common factor is x. We get:
x(x + 6) + 7(x + 6)

Step 5: Notice that we have a common binomial factor of (x + 6) in both groups. We can factor that out:
(x + 6)(x + 7)

Therefore, the expression x^2 + 13x + 42 in factored form is (x + 6)(x + 7).

Answer 3

[AI-generated answer — Explain Bot]

To find the expression in factored form, you need to factorize the quadratic equation x^2 + 13x + 42.

Step 1: Look for two numbers that can multiply to give the constant term (42) and add up to give the coefficient of the middle term (13). In this case, the numbers are 6 and 7.

Step 2: Rewrite the middle term (13x) using these two numbers:
x^2 + 6x + 7x + 42

Step 3: Group the terms:
(x^2 + 6x) + (7x + 42)

Step 4: Factor out the greatest common factor from each group:
x(x + 6) + 7(x + 6)

Step 5: Notice that both groups have a common factor of (x + 6). Factor it out:
(x + 6)(x + 7)

Therefore, the expression x^2 + 13x + 42 in factored form is (x + 6)(x + 7).