Video Transcript
Factorize fully 𝑥 squared 𝑦
squared minus three 𝑥𝑦 squared minus 108𝑦 squared.
We notice immediately that every
term of this trinomial has a factor of 𝑦 squared. Pulling this factor out, we have 𝑦
squared times a quadratic in 𝑥. To factor this quadratic, we need
to find two numbers whose product is 108 and whose sum is negative three.
Observe that 108 equals 12 times
nine and that nine minus 12 equals negative three. Thus, 𝑥 squared minus three 𝑥
minus 108 factors as 𝑥 plus nine times 𝑥 minus 12. The given degree for polynomial is
now fully factored as a product of four linear factors.
