Use grouping to factor out the polynomial.2ab+4a+3b2+6b2ab+4a+3b^2+6b

( b + 2 ) ( 2 a + 3 b ) \left(b+2\right)\left(2a+3b\right) ( b + 2 ) ( 2 a + 3 b )

Use grouping to factor out the polynomial. 2 a b + 4 a + 3 b 2 + 6 b 2ab+4a+3b^2+6b

To factor by grouping, we first need to pair up the terms in our polynomial and then identify the greatest common factor for each pair. So let's start by trying to pair the first two terms and the last two terms. Do these pairings have a greatest common factor? Well, between two a b and four a, we do have a greatest common factor of two a. And between three b squared and six b, we also have a greatest common factor here of three b. So now that we've identified our greatest common factor for each pairing, we can go ahead and factor it out of each pair. So factoring out two a from our first two terms, we're left with b plus two. And factoring out three b from our last two terms, we are also left with b plus two, which is perfect because now we have a common binomial that we can also factor out. So factoring out b plus two, we're left with two a plus three b. And this here is our final answer of our same polynomial now in factored form.

Use grouping to factor out the polynomial. 2 a b + 4 a + 3 b 2 + 6 b 2ab+4a+3b^2+6b

( b + 2 ) ( 2 a + 3 b ) \left(b+2\right)\left(2a+3b\right) ( b + 2 ) ( 2 a + 3 b )

( 2 a + 3 ) ( b + 2 ) \left(2a+3\right)\left(b+2\right) ( 2 a + 3 ) ( b + 2 )

( 2 a + b ) ( b + 6 ) \left(2a+b\right)\left(b+6\right) ( 2 a + b ) ( b + 6 )

( a + 3 b ) ( 2 b + 2 ) \left(a+3b\right)\left(2b+2\right) ( a + 3 b ) ( 2 b + 2 )

7. Factoring

Factoring by Greatest Common Factor & Grouping

Intermediate Algebra

7. Factoring

Factoring by Greatest Common Factor & Grouping

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Multiple Choice

Use grouping to factor out the polynomial.
$2 a b + 4 a + 3 b^{2} + 6 b$

$\left(2a+3\right)\left(b+2\right)$

$\left(2a+b\right)\left(b+6\right)$

$\left(b+2\right)\left(2a+3b\right)$

$\left(a+3b\right)\left(2b+2\right)$

Verified step by step guidance

Group the polynomial into two pairs to make factoring easier: group the first two terms and the last two terms separately. So, write it as $\left(2ab + 4a\right) + \left(3b^2 + 6b\right)$.

Factor out the greatest common factor (GCF) from each group. From the first group \$2ab + 4a$, factor out $2a$ to get $2a(b + 2)$. From the second group $3b^2 + 6b$, factor out $3b$ to get $3b(b + 2)$.

Notice that both groups now contain the common binomial factor $(b + 2)$. This is key to factoring by grouping.

Factor out the common binomial factor $(b + 2)$ from the entire expression, which gives you $(b + 2)(2a + 3b)$.

Verify your factorization by expanding the factors back out to ensure it matches the original polynomial.

5:47m

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