Factor the polynomial. Please show all work.
x^2+2x-3
+3-1 = +2
so
(x+3)(x-1)
thanks so much - but I have no idea what you did. why is it +3-1=2. How did you get to this? Is there a rule?
I was looking for what with 3 would make 2 and it is one.
To factor the polynomial x^2 + 2x - 3, we need to find two numbers whose product is equal to the product of the first and last terms (in this case, -3), and whose sum or difference is equal to the coefficient of the middle term (in this case, 2x).
In this case, the numbers we are looking for are 3 and 1, because 3 * 1 = 3 and 3 + 1 = 4 (the middle term coefficient is 2x), with the condition that one of the numbers should be negative.
Now, we rewrite the middle term using these two numbers:
x^2 + 3x - x - 3
Next, we group the terms in pairs and factor out the greatest common factor from each pair:
(x^2 + 3x) - (x + 3)
Now, we factor out the common terms from each pair:
x(x + 3) - 1(x + 3)
Finally, we factor out the common binomial: (x + 3)
(x + 3)(x - 1)
Therefore, the factored form of the polynomial x^2 + 2x - 3 is (x + 3)(x - 1).