Questions: Factor the four-term polynomial by grouping. 5x^2-15xy-3x+9y Select the correct choice below and, if necessary, fill in the answer box within your choice. A. 5x^2-15xy-3x+9y= B. The polynomial is not factorable by grouping.

Factor the four-term polynomial by grouping.

5x^2-15xy-3x+9y

Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. 5x^2-15xy-3x+9y=
B. The polynomial is not factorable by grouping.

Transcript text: Factor the four-term polynomial by grouping. \[ 5 x^{2}-15 x y-3 x+9 y \] Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $5 x^{2}-15 x y-3 x+9 y=$ $\square$ B. The polynomial is not factorable by grouping.

Solution

Solution Steps

To factor the given four-term polynomial by grouping, we first split the polynomial into two groups. Then, we factor out the greatest common factor (GCF) from each group. Finally, we check if the remaining binomials are identical, which allows us to factor them out as a common factor.

Step 1: Group the Terms

We start with the polynomial: \[ 5x^2 - 15xy - 3x + 9y \] We can group the terms as follows: \[ (5x^2 - 15xy) + (-3x + 9y) \]

Step 2: Factor Out the GCF from Each Group

Next, we factor out the greatest common factor (GCF) from each group: \[ 5x(x - 3y) - 3(x - 3y) \]

Step 3: Factor Out the Common Binomial

Now, we notice that $(x - 3y)$ is a common factor: \[ (5x - 3)(x - 3y) \]