Find all integers b such that the trinomial $x ^ { 2 } + b x + 10$ can be factored.
A) $\pm 7 , \pm 11$
B) 10,1
C) $\pm 2 , \pm 5$
D) -2,-5
E) -7,-11

Question

Quizplus · Accepted Answer

For a trinomial $x^2 + bx + 10$ to be factored, the factors of the constant term (10) must add up to the middle coefficient $b$. The factors of 10 are 1 and 10, or 2 and 5, which can be either positive or negative. Adding these factors gives possible $b$ values of $\pm 11$ (from $\pm 1$ and $\pm 10$) and $\pm 7$ (from $\pm 2$ and $\pm 5$).

Find All Integers B Such That the Trinomial x2+bx+10x ^ { 2 } + b x + 10x2+bx+10

Find All Integers B Such That the Trinomial $x ^ { 2 } + b x + 10$