Factor completely. Remember to look first for a common factor. Check by multiplying. If a polynomial is prime state this.
a^2-2ab-3b^2
What would lead to a product of -3? (1,-3 or -1,3)
From the two end terms, what would add to -2? Since the first term has to be 1, the last term has to be -3 to = -2. Include the a and b terms.
I hope this helps.
To factor the polynomial a^2 - 2ab - 3b^2 completely, we can first look for common factors. In this case, there are no common factors.
Next, we can try to factor it using the quadratic factoring method. We need to find two numbers that multiply to give us -3b^2 and add up to -2ab. In this case, we can see that -3b^2 can be factored as -3b * b, and -2ab can be factored as -3b * a + b * a. So, our factors will be (a - 3b) and (a + b).
Thus, the completely factored form of the polynomial a^2 - 2ab - 3b^2 is (a - 3b)(a + b).