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

Intermediate Algebra

7. Factoring

Factoring by Greatest Common Factor & Grouping

Struggling with Intermediate Algebra?

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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: group the first two terms and the last two terms separately, like this: $\left(xy + 2x\right) + \left(3y + 6\right)$.

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

Notice that both groups now contain the common binomial factor $(y + 2)$. This allows you to factor by grouping.

Factor out the common binomial factor $(y + 2)$ from the entire expression, resulting in $(x + 3)(y + 2)$.

Verify your factorization by expanding $(x + 3)(y + 2)$ to ensure it matches the original polynomial $xy + 2x + 3y + 6$.

5:47m

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