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

• A. $(x+2y)(3x+y)$
• B. $(2x+y)(x+3y)$
• C. $(2x-y)(x+3y)$
• D. $(x+3y)(2x+y)$

Answer: (B)

Verified step by step guidance

1. Identify the polynomial to factor: \$2x^{2} + 7xy + 3y^{2}$.
2. Look for two binomials of the form \((ax + by)(cx + dy)\) whose product equals the original polynomial.
3. Find two numbers that multiply to the product of the first and last coefficients: \(2 \times 3 = 6\), and add up to the middle coefficient, 7.
4. Use these numbers to split the middle term and then group terms to factor by grouping.
5. Factor out the common binomial from each group to write the polynomial as the product of two binomials: \((2x + y)(x + 3y)\).