What is the expression in factored form?
x2+13x+42 show all work
To find the expression in factored form, we need to factor the quadratic equation x^2 + 13x + 42.
First, we find two numbers that multiply to give the constant term (42) and add up to give the coefficient of the middle term (13).
The numbers in this case are 6 and 7 because 6*7 = 42 and 6 + 7 = 13.
Then, we rewrite the middle term (13x) as the sum of the two selected numbers (6x + 7x):
x^2 + 6x + 7x + 42
We can now group the terms:
(x^2 + 6x) + (7x + 42)
From each group, we can factor out the greatest common factor:
x(x + 6) + 7(x + 6)
Now, we can see that we have a common binomial factor of (x + 6):
(x + 6)(x + 7)
So, the expression in factored form is (x + 6)(x + 7).