polynomials factoring

Question

 

x² +11x +30

 

Answer 1

Your factored form will be

 

(x + r)(x + q)

 

where  r and q are integers

 

such that

 

rq = 30

r + q = 11

 

Find these value of r and q.

 

 

Any questions?

Answer 2

You should be given some strategies by your teacher.

 

This quadratic has the sign of the last term positive, and that means the signs in the middle of each binomial factor will be the same; the negative sign of the trinomial's middle term means that those signs (in binomials' middles) will be negative.

 

Then it's just a matter of splitting the 30 into two factors whose sum is 11.

 

Thus the answer is (x-5)(x-6).

 

Finally, check by using FOIL.

 

POSTSCRIPT: I thought that the question had a negative coefficient on its linear term!!  (Did my eyes deceive me?)