Factor the trinomial: 5x^(2)+11 x+6 Answer:

Identify Structure: Identify the structure of the trinomial. The trinomial is in the form ax^2 + bx + c, where a = 5, b = 11, and c = 6.Find Multiplying Numbers: Look for two numbers that multiply to ac (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 fit this requirement because 5 * 6 = 30 and 5 + 6 = 11.Rewrite Middle Term: Rewrite the middle term (11x) using the two numbers found in Step 2. The trinomial 5x^2 + 11x + 6 can be rewritten as 5x^2 + 5x + 6x + 6.Factor by Grouping: Factor by grouping. Group the terms into two pairs: (5x^2 + 5x) and (6x + 6).Factor out Common Factor: Factor out the greatest common factor from each group. From the first group (5x^2 + 5x), factor out 5x to get 5x(x + 1). From the second group (6x + 6), factor out 6 to get 6(x + 1).Write Final Factored Form: Write down the final factored form. Since both groups contain the common factor (x + 1), the trinomial can be factored as (5x + 6)(x + 1).

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Q. Factor the trinomial:

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5 x^{2}+11 x+6

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Answer:

Identify Structure: Identify the structure of the trinomial. $\newline$ The trinomial is in the form $ax^2 + bx + c$ , where $a = 5$ , $b = 11$ , and $c = 6$ .
Find Multiplying Numbers: Look for two numbers that multiply to $ac$ ( $5 \times 6 = 30$ ) and add up to $b$ ( $11$ ). $\newline$ We need to find two numbers that multiply to $30$ and add up to $11$ . The numbers $5$ and $6$ fit this requirement because $5 \times 6 = 30$ and $5 + 6 = 11$ .
Rewrite Middle Term: Rewrite the middle term $11x$ using the two numbers found in Step $2$ . $\newline$ The trinomial $5x^2 + 11x + 6$ can be rewritten as $5x^2 + 5x + 6x + 6$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the terms into two pairs: $(5x^2 + 5x)$ and $(6x + 6)$ .
Factor out Common Factor: Factor out the greatest common factor from each group. $\newline$ From the first group $5x^2 + 5x$ , factor out $5x$ to get $5x(x + 1)$ . $\newline$ From the second group $6x + 6$ , factor out $6$ to get $6(x + 1)$ .
Write Final Factored Form: Write down the final factored form. $\newline$ Since both groups contain the common factor $(x + 1)$ , the trinomial can be factored as $(5x + 6)(x + 1)$ .