How would you factorize a polynomial?

Question

Mathematics

Hello! Explain (no need to solve!) please how to factorize the following polynomials:
1) p ² +pq-2q ² ;
2) 2m-m ² -1 + n ² ;
3) y ³ -5y ² -2y+16.
Thank you.

Answer 1

The general principle is to find the roots x ₁ ...x _n and represent the polynomial in the form (xx ₁ )*(xx ₂ )*...*(xx _n )
The roots can be found both by selection and by analytical methods. For example, the first polynomial:
p ² +pq-2q ² = 0
D = q ² +8q ² = 9q ²
p ₁ = (-q+3q)/2 = q
p ₂ = (-q-3q)/2 = - 2q
p ² +pq-2q ² = (pq)*(p+2q)
PS.
You can solve sequentially, choosing one root x _iand dividing the polynomial by (xx _i )