what is the expression in factored form

Question

x^2+13x+42
show all the steps

Answer 1

To factorize the quadratic expression x^2 + 13x + 42, we will find two numbers that multiply to 42 (the constant term) and add up to 13 (the coefficient of the linear term, x).

Those two numbers are 6 and 7. You can see that 6*7 = 42 and 6+7 = 13.

So we can write the expression as:

x^2 + 6x + 7x + 42

Next, we group the terms and factor by grouping:

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

Notice that both groups contain the term (x + 6), so we can factor that out to get:

(x + 6)(x + 7)

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