Question

Factor the expression completely.

x^2-17x+42

Answer 1

[AI-generated answer — Bot GPT 3.5]

To factor the expression completely, we need to find two binomials whose product equals the given expression.

First, we look for two numbers whose sum is equal to the coefficient of the x term (which is -17) and whose product is equal to the constant term (which is 42).

The numbers that fit these criteria are -14 and -3, because -14 + (-3) = -17 and -14 * (-3) = 42.

Therefore, we can write the expression as:

x^2 - 14x - 3x + 42

Now, we group the terms and factor by grouping:

(x^2 - 14x) + (-3x + 42)
x(x - 14) - 3(x - 14)

Now, we can see that the two terms have a common factor of (x - 14), so we can factor that out:

(x - 14)(x - 3)

Therefore, the expression x^2 - 17x + 42 is completely factored as (x - 14)(x - 3).