Questions: Factor the following polynomial. 18 x y+21 x+6 y+7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 18 x y+21 x+6 y+7= (Factor completely.) B. The polynomial has no common factor other than 1.

Solution Steps

To factor the given polynomial \(18xy + 21x + 6y + 7\), we can use the method of grouping. First, we group the terms in pairs and factor out the greatest common factor from each pair. Then, we look for a common binomial factor in the resulting expression.

We start with the polynomial \(18xy + 21x + 6y + 7\). To factor it, we can group the terms as follows: \[ (18xy + 21x) + (6y + 7) \]

Next, we factor out the greatest common factor from each group:

• From the first group \(18xy + 21x\), we can factor out \(3x\): \[ 3x(6y + 7) \]
• From the second group \(6y + 7\), there is no common factor to factor out.

Thus, we rewrite the polynomial as: \[ 3x(6y + 7) + 1(6y + 7) \]

Now, we notice that both terms contain the common binomial factor \((6y + 7)\). We can factor this out: \[ (3x + 1)(6y + 7) \]

Final Answer