Question

You are factoring $x^2+11x-26$ . What do the signs of the terms tell you about the factors? Explain.

Answer 1

think about FOIL. first, outer, inner, last.

(x+a)(x+b)

first terms: x*x = x^2
inner terms: a*x
outer terms: b*x
last terms: a*b

sum to get x^2 + ax + bx + ab

compare this to your original expression. x^2+11x-26. the constant term is negative. notice how the product of a*b is equal to the constant term. that means a and b must have opposite signs. (one must be positive, the other must be negative. otherwise, if they were both positive or both negative, a*b would be positive.)

is there anything else you can conclude? what about the sign of the x^2 term or the value of ax + bx?