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)

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

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

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

7. Factoring

Factoring by Greatest Common Factor & Grouping

Beginning Algebra

7. Factoring

Factoring by Greatest Common Factor & Grouping

Struggling with Beginning 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.
$x y + 2 x + 3 y + 6$

$(x + 3) (y + 2)$

$(x + 2) (y + 3)$

$(x + 3) (y + 6)$

$(x + 2) (y + 6)$

Verified step by step guidance

Start with the polynomial: $xy + 2x + 3y + 6$.

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

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

Notice that both groups contain the common binomial factor $(y + 2)$, so factor this out: $(x + 3)(y + 2)$.

The polynomial is now factored as the product of two binomials: $(x + 3)(y + 2)$.

5:47m

Watch next

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

Start learning