Question

In the following exercises, factor each trinomial of the form $x^2+bxy+c{y}^2$

$x^2-3xy-14y^2$

Short answer

The factorization of the expression $x^2-3xy-14y^2$is not factorable.

Step-by-step solution

Step 1. Given information

Given expression is$x^2-3xy-14y^2$

Step 2. Find the last terms of the trinomials.

The factors of the expression:

Factors of -14	Sum of factor
2, -7	2 + (-7) = -5
-2, 7	-2 + 7 = 5
7, -1	7 + (-1) = 6
-7, 1	-7 + 1 = -6

Step 3. Factorization

Among the pair of numbers, there are no pairs with the sum of$-3$.

The given expression$x^2-3xy-14y^2$is not factorable, because the trinomial is prime.