Use grouping to factor out the polynomial.xy+2x+3y+6xy+2x+3y+6

( x + 3 ) ( y + 2 ) \left(x+3\right)\left(y+2\right) ( x + 3 ) ( y + 2 )

Use grouping to factor out the polynomial. x y + 2 x + 3 y + 6 xy+2x+3y+6

To factor by grouping, our first step is to pair up the terms in our four term polynomial and see if those pairs of terms have a greatest common factor. So let's start with our first two terms and last two terms. Do these groupings have a greatest common factor? Well, the greatest common factor between x, y, and two x is x. And the greatest common factor between three y and six is three, which is perfect. Now that each of them have a greatest common factor, we can factor those out of each pairing. Factoring out x from x y plus two x, we're left with y plus two, and factoring out three from 3y plus six, we're left with y plus two, which is perfect because now we have a common binomial between each of our terms, and we can also factor it out. So, factoring out y plus two, we're left with x plus three, and this here is our final answer. It's our same polynomial now in factored form.

Use grouping to factor out the polynomial. x y + 2 x + 3 y + 6 xy+2x+3y+6

( x + 3 ) ( y + 2 ) \left(x+3\right)\left(y+2\right) ( x + 3 ) ( y + 2 )

( x + 2 ) ( y + 3 ) \left(x+2\right)\left(y+3\right) ( x + 2 ) ( y + 3 )

( x + 3 ) ( y + 6 ) \left(x+3\right)\left(y+6\right) ( x + 3 ) ( y + 6 )

( x + 2 ) ( y + 6 ) \left(x+2\right)\left(y+6\right) ( x + 2 ) ( y + 6 )

7. Factoring

Factoring by Greatest Common Factor & Grouping

Beginning & Intermediate Algebra

7. Factoring

Factoring by Greatest Common Factor & Grouping

Struggling with Beginning & Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Use grouping to factor out the polynomial.
$x y + 2 x + 3 y + 6$

$\left(x+3\right)\left(y+2\right)$

$\left(x+2\right)\left(y+3\right)$

$\left(x+3\right)\left(y+6\right)$

$\left(x+2\right)\left(y+6\right)$

Verified step by step guidance

Group the terms in pairs to make factoring easier: write the polynomial as $(xy + 2x) + (3y + 6)$.

Factor out the greatest common factor (GCF) from each group separately. From the first group $(xy + 2x)$, factor out $x$ to get $x(y + 2)$. From the second group $(3y + 6)$, factor out \$3$ to get $3(y + 6)$.

Notice that the binomials inside the parentheses are not the same yet, so check if rearranging the original terms helps. Try grouping as $(xy + 3y) + (2x + 6)$ instead.

Factor out the GCF from the new groups: from $(xy + 3y)$ factor out $y$ to get $y(x + 3)$, and from $(2x + 6)$ factor out \$2$ to get $2(x + 3)$.

Now you have a common binomial factor $(x + 3)$ in both terms, so factor it out: $(x + 3)(y + 2)$.

5:47m

Watch next

Master Factoring the GCF out of Polynomials with a bite sized video explanation from Patrick Ford

Start learning