Question

Find constants p and q such that x^4-2x^3-x^2+2x+10=(x^2+px+5)(x^2+qx+2)

Answer 1

p = -4 q = 2

Explanation:

1. Expand the brackets ( yes the entire thing).
2. group together the values with same co-effiecients; like (q+p)x^3 etc etc.
3. equate the co-effiecients on the left hand side to the now grouped ones on the right, for example [x^3]: -2x^3= (q+p)x^3, the x^3 cancels and ull get an equation only in terms of p and q. do the same for [x] and ull get an equation with only q, solve this and get the value for q [q = 2].
4. sub in this value for the [x^3] equation and ull get an answer for p [p= -4].

hope my explanation is understandable lol