what is the polynomials factor of b2 + 8b + 7?

Question

how do i solve this problem i dont understand how to do it

Answer 1

( b + m ) ( b + n) =

 

  ( b + m) b + n ( b+ m) = b^2 + mb + nb + nm = b^2  +( m+n )b + mn

 

      You m, n should be such that:

     

      m+ n = 8

      mn = 7

 

        turns out: m=7, n =1   

Answer 2

You're being asked to factor this polynomial b² + 8b + 7 into two factors (binomials). If you "FOIL" or redistribute the two binomials, you should obtain the original polynomial.

 

With this idea, what are the factors of b²? Just b*b. So the first terms of your factors will be:

(b +  )(b +  )

You notice I filled in the +'s because the original problem had two +'s.

 

Now what are the factors of 7? Just 7*1, so now we fill that in and we are done!

(b + 7)(b + 1)