Step 1

Given polynomial is \(b^{2}-8b+7\)

To factor the given polynomial.

Solution:

We will use middle term term split method.

In middle term split method, middle term is sum of two factors and product of two factors is equal to product of first and last term.

Factorizing the given polynomial.

\(b^{2}-8b+7=b^{2}-7b-b+7\)

\(=b(b-7)-1(b-7)\)

\(=(b-7)(b-1)\)Therefore, \(b^{2}-8b+7=(b-7)(b-1)\).

Step 2

Hence, required factor is \(b^{2}−8b+7=(b−7)(b−1)\).