Question

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

$c^2-7cd+18d^2$

Short answer

The factorization of the expression$c^2-7cd+18d^2$is not factorable.

Step-by-step solution

Step 1. Given information

Given expression is$c^2-7cd+18d^2$

Step 2. Find the last terms of the trinomials.

The factors of the expression:

Factors of 18	Sum of factors
-9, -2	-9 + (-2) = -11
-6, -3	-6 + (-3) = -9
-18, -1	-18 + (-1) = -19

Step 3. Factorization

Among the pair of numbers, there are no pairs with the sum of $-7$

The given expression $c^2-7cd+18d^2$is not factorable, because the trinomial is prime.