Question

question 1-8
the polynomial ( a^2 - 7a + 2ab - 14b ) can be factored into ( a - 7 ) and ______.
( circ a - 2b )
( circ a + 2b )
( circ 2(a + 2b) )
( circ a(a + 2) )

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms of the polynomial:
\( (a^2 - 7a) + (2ab - 14b) \)

Step2: Factor out the GCF from each group

Factor out \( a \) from the first group and \( 2b \) from the second group:
\( a(a - 7) + 2b(a - 7) \)

Step3: Factor out the common binomial factor

Now, factor out \( (a - 7) \) from both terms:
\( (a - 7)(a + 2b) \)

So the polynomial \( a^2 - 7a + 2ab - 14b \) factors into \( (a - 7) \) and \( (a + 2b) \).

Answer:

B. \( a + 2b \)