Problem 61 - Introductory Algebra for College Students

Question

Factor each polynomial using the greatest common binomial factor. $$x(y+6)-7(y+6)$$

Step-by-Step Solution

Answer

The factored form of the polynomial \(x(y+6)-7(y+6)\) is \((y+6)(x-7)\).

Step 1: Identify Common Binomial Factor

In the given polynomial \(x(y+6)-7(y+6)\) the common binomial to both terms is \((y+6)\).

Step 2: Factor out the common binomial factor

Factoring out a common binomial factor involves using the distributive property, which states that in the expression \(a(b + c)\) it equals to \(ab + ac\). If we apply this rule in reverse to the exercise, we will get the factored form by taking \((y + 6)\) as a common factor. The expression \(x(y+6)-7(y+6)\) then becomes \((y+6)(x-7)\).