Question Video: Factorizing Trinomials by Taking Out the Greatest Common Factor Mathematics • Second Year of Preparatory School

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.