Factor the expression. 6x^(2)+7x+2

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 6x^2 + 7x + 2, which is in the form ax^2 + bx + c. a = 6, b = 7, c = 2Find numbers for multiplication: Find two numbers that multiply to a*c (6*2=12) and add up to b (7). The numbers that satisfy these conditions are 3 and 4, since 3*4 = 12 and 3+4 = 7.Rewrite middle term: Rewrite the middle term (7x) using the two numbers found in the previous step, splitting it into two terms (3x and 4x). The expression becomes 6x^2 + 3x + 4x + 2.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (6x^2 + 3x) + (4x + 2)Factor out common factor: Factor out the greatest common factor from each group. 3x(2x + 1) + 2(2x + 1)Since both groups contain the common factor (2x + 1), factor this out. (3x + 2)(2x + 1)

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Q. Factor the expression.

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6 x^{2}+7 x+2

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $6x^2 + 7x + 2$ , which is in the form $ax^2 + bx + c$ . $\newline$ $a = 6$ , $b = 7$ , $c = 2$
Find numbers for multiplication: Find two numbers that multiply to $a*c$ ( $6*2=12$ ) and add up to $b$ ( $7$ ). $\newline$ The numbers that satisfy these conditions are $3$ and $4$ , since $3*4 = 12$ and $3+4 = 7$ .
Rewrite middle term: Rewrite the middle term $7x$ using the two numbers found in the previous step, splitting it into two terms $3x$ and $4x$ . The expression becomes $6x^2 + 3x + 4x + 2$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(6x^2 + 3x) + (4x + 2)$
Factor out common factor: Factor out the greatest common factor from each group. $3x(2x + 1) + 2(2x + 1)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $3x(2x + 1) + 2(2x + 1)$ Since both groups contain the common factor $(2x + 1)$ , factor this out. $\newline$ $(3x + 2)(2x + 1)$