Factor the following polynomial2x2+7xy+3y22x^2+7xy+3y^2

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

Factor the following polynomial 2 x 2 + 7 x y + 3 y 2 2x^2+7xy+3y^2

For this problem, we've been asked to factor this trinomial. And to do this, we're going to use the AC method or grouping method that we've been learning so far. So our first step is to identify our a and c value, as well as our b value. And we want to find two numbers that multiply to our a times c value of six and also add to our b value of seven. So those two numbers are one and six, which make seven. So we're going to use this pair of factors to split apart the middle term of our trinomial here. Doing that, we have 2x squared plus 1xy plus 6xy plus 3y squared. And now we can apply factoring by grouping to this polynomial. We're going to group our first two terms and our last two terms and check to make sure that they each have a greatest common factor. For our first two terms, they have a greatest common factor of x and for our last two terms, they have a greatest common factor of three y. So now we can factor out those greatest common factors from each pairing. So factoring out x, we're left with two x plus y, and factoring out three y, we're left with two x plus y as well. And now that we have a common binomial, we can also factor it out. So factoring out two x plus y, we're left with x plus three y. And this here is our final answer.

Factor the following $$polynomial2x2+7xy+3y22x^2$+7xy+3y^2$$

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

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

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

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

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7. Factoring

Factoring Trinomials of the Form ax² + bx + c

Intermediate Algebra

7. Factoring

Factoring Trinomials of the Form ax² + bx + c

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객관식

Factor the following polynomial
$2 x^{2} + 7 x y + 3 y^{2}$

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

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

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

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

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Identify the polynomial to factor: $2x^2 + 7xy + 3y^2$.

Look for two binomials of the form $(ax + by)(cx + dy)$ whose product gives the original polynomial.

Multiply the first terms: $a \times c = 2$ (coefficient of $x^2$), and the last terms: $b \times d = 3$ (coefficient of $y^2$).

Find pairs of numbers for $a$ and $c$ that multiply to 2, and for $b$ and $d$ that multiply to 3, then test combinations to get the middle term \$7xy$ by using the distributive property: $ad + bc = 7$.

Once the correct pair is found, write the factored form as $(2x + y)(x + 3y)$ or equivalent, confirming by expanding to check it matches the original polynomial.