 # Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary: b^{2}-8b+7 Caelan 2021-05-30 Answered
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary:
${b}^{2}-8b+7$
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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.
${b}^{2}-8b+7={b}^{2}-7b-b+7$
$=b\left(b-7\right)-1\left(b-7\right)$
$=\left(b-7\right)\left(b-1\right)$Therefore, ${b}^{2}-8b+7=\left(b-7\right)\left(b-1\right)$.
Step 2
Hence, required factor is ${b}^{2}-8b+7=\left(b-7\right)\left(b-1\right)$.