Question
Factor.
x, squared, plus, 2, x, minus, 15
x
2
+2x−15
x, squared, plus, 2, x, minus, 15
x
2
+2x−15
Answers
GPT 3.5
To factor the expression x^2 + 2x - 15, we need to find two numbers whose product is -15 and whose sum is 2.
The numbers that satisfy these conditions are 5 and -3, since 5 * -3 = -15 and 5 + -3 = 2.
Now we can rewrite the expression as:
x^2 + 5x - 3x - 15
Next, we group the terms and factor by grouping:
(x^2 + 5x) - (3x + 15)
x(x + 5) - 3(x + 5)
Finally, we can factor out the common binomial (x + 5):
(x + 5)(x - 3)
Therefore, the factored form of x^2 + 2x - 15 is (x + 5)(x - 3).
The numbers that satisfy these conditions are 5 and -3, since 5 * -3 = -15 and 5 + -3 = 2.
Now we can rewrite the expression as:
x^2 + 5x - 3x - 15
Next, we group the terms and factor by grouping:
(x^2 + 5x) - (3x + 15)
x(x + 5) - 3(x + 5)
Finally, we can factor out the common binomial (x + 5):
(x + 5)(x - 3)
Therefore, the factored form of x^2 + 2x - 15 is (x + 5)(x - 3).