Final answer:
To factor the polynomial ab + 2a + 4b + 8, we group the terms into (ab + 2a) and (4b + 8), then factor out the common terms resulting in the factored form (a + 4)(b + 2).
Step-by-step explanation:
The question asks us to factor the given polynomial by grouping. The polynomial in question is ab + 2a + 4b + 8. To factor by grouping, we usually look for common factors in pairs of terms. Let's break it down into steps:
Group the terms with common factors: (ab + 2a) + (4b + 8).Factor out the common factor in each group: a(b + 2) + 4(b + 2).Recognize that (b + 2) is now a common factor and can be factored out: (a + 4)(b + 2).
Thus, the polynomial ab + 2a + 4b + 8 can be factored into (a + 4)(b + 2).