Question

PLEASE HELP!! Factor the polynomial x^2 - 14x + 49 as the product of two binomials.

x^2 - 14x + 49 = (x + A)(x + B)

I thought, A and B were both 7, but it's saying that's wrong. Could someone please help and explain how you got the answer?

Answer 1

x^2+14x+49=(x+7)^2

Explanation:

This is factoring using perfect squares. The leading coefficient is 1, which is a perfect square, and the constant is 49 which is also a perfect square. 7 is correct, but I'm wondering if your sings are off. Look at the quadratic. The second sign, plus or minus I mean, is a +. That means that both the signs in your parenthesis are going to be the same. The sign that they are both going to be is whatever the first sign is. Ours is negative. So your factors are (x - 7)(x - 7). That trick works as long as the second sign is a positive. If the second sign is negative, the only thing we know for sure is that both signs will be different (one positive and one negative).

Answer 2

This is factoring using perfect squares. The leading coefficient is 1, which is a perfect square, and the constant is 49 which is also a perfect square. 7 is correct, but I'm wondering if your sings are off. Look at the quadratic. The second sign, plus or minus I mean, is a +. That means that both the signs in your parenthesis are going to be the same. The sign that they are both going to be is whatever the first sign is. Ours is negative. So your factors are (x - 7)(x - 7). That trick works as long as the second sign is a positive. If the second sign is negative, the only thing we know for sure is that both signs will be different (one positive and one negative).