Given $x ^ { 2 } + b x + c$ , if no two factors of c produce a sum of b , then the trinomial is not factorable using integers.

Question

Quizplus · Accepted Answer

This statement is known as the "zero product property." If a trinomial is factorable using integers, then it can be written as the product of two binomials in the form $(x + m)(x + n)$, where m and n are integers that add up to b and multiply to c. However, if no two factors of c produce a sum of b, then it is impossible to find values of m and n that satisfy the equation $$m + n = b$$ Therefore, the trinomial cannot be factored using integers.

Given x2+bx+cx ^ { 2 } + b x + cx2+bx+c

Given $x ^ { 2 } + b x + c$