Factor completely. 5x^(2)+11 x+6 Answer:

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 5x^2 + 11x + 6. The quadratic expression is in the form ax^2 + bx + c, where: a = 5 b = 11 c = 6Find two numbers: Find two numbers that multiply to a*c (5*6 = 30) and add up to b (11). We need to find two numbers that multiply to 30 and add up to 11. The numbers 5 and 6 satisfy these conditions because: 5 * 6 = 30 5 + 6 = 11Write middle term: Write the middle term 11x as a sum of two terms using the numbers 5 and 6. We can express 11x as 5x + 6x, so the expression becomes: 5x^2 + 5x + 6x + 6Factor by grouping: Factor by grouping. Group the terms into two pairs and factor out the common factors: (5x^2 + 5x) + (6x + 6) Factor out 5x from the first group and 6 from the second group: 5x(x + 1) + 6(x + 1)Factor out common binomial: Factor out the common binomial factor (x + 1). Since both groups contain the factor (x + 1), we can factor it out: (5x + 6)(x + 1)

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Factor completely.

5x^(2)+11 x+6
Answer:

Factor completely. $\newline$ $5 x^{2}+11 x+6$ $\newline$ Answer:

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Q. Factor completely.

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5 x^{2}+11 x+6

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Answer:

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $5x^2 + 11x + 6$ . The quadratic expression is in the form $ax^2 + bx + c$ , where: $a = 5$ $b = 11$ $c = 6$
Find two numbers: Find two numbers that multiply to $a*c$ ( $5*6 = 30$ ) and add up to $b$ ( $11$ ). $\newline$ We need to find two numbers that multiply to $30$ and add up to $11$ . $\newline$ The numbers $5$ and $6$ satisfy these conditions because: $\newline$ $5 * 6 = 30$ $\newline$ $5 + 6 = 11$
Write middle term: Write the middle term $11x$ as a sum of two terms using the numbers $5$ and $6$ . We can express $11x$ as $5x + 6x$ , so the expression becomes: $5x^2 + 5x + 6x + 6$
Factor by grouping: Factor by grouping. $\newline$ Group the terms into two pairs and factor out the common factors: $\newline$ $(5x^2 + 5x) + (6x + 6)$ $\newline$ Factor out $5x$ from the first group and $6$ from the second group: $\newline$ $5x(x + 1) + 6(x + 1)$
Factor out common binomial: Factor out the common binomial factor $(x + 1)$ . Since both groups contain the factor $(x + 1)$ , we can factor it out: $(5x + 6)(x + 1)$