Question

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

Explanation:

Step1: Factor by grouping

Group the terms of the polynomial: \((a^2 - 7a)+(2ab - 14b)\)
Factor out the greatest common factor from each group: \(a(a - 7)+2b(a - 7)\)

Step2: Factor out the common binomial factor

Now, factor out the common binomial factor \((a - 7)\) from the two terms: \((a - 7)(a + 2b)\)
So the polynomial \(a^2 - 7a + 2ab - 14b\) can be factored into \((a - 7)\) and \(a + 2b\).

Answer:

B. \(a + 2b\)