If possible, completely factor the expression. (If the polynomial is not factorable using integers, enter PRIME.)
x^2+17 x+70
can you think of two numbers which when multiplied give you 70 and which add up to 17 ?
To completely factor the expression x^2 + 17x + 70, we need to find two binomials that, when multiplied together, equal the given expression.
1. First, we look at the coefficient of the x^2 term, which is 1. We know that the binomial factors will start with (x + ?)(x + ?).
2. Next, we need to find two numbers that multiply to give 70 (the constant term) and add up to 17 (the coefficient of the x term).
The pairs of numbers that satisfy these conditions are (5, 14) and (7, 10).
3. We can try both pairs to see which one works.
Let's start with the pair (5, 14):
(x + 5)(x + 14)
Expanding this:
x * x = x^2
x * 14 = 14x
5 * x = 5x
5 * 14 = 70
So, (x + 5)(x + 14) is the factored form of the expression x^2 + 17x + 70.
Therefore, the complete factorization of x^2 + 17x + 70 is (x + 5)(x + 14).