Factor the trinomial: 2x^(2)+11 x+12 Answer:

Identify a, b, c: Identify a, b, and c in the trinomial 2x^2 + 11x + 12. Compare 2x^2 + 11x + 12 with ax^2 + bx + c. a = 2 b = 11 c = 12Find product and sum: Find two numbers whose product is a*c (2*12 = 24) and whose sum is b (11). We need to find two numbers that multiply to 24 and add up to 11. The numbers 8 and 3 satisfy these conditions because: 8 * 3 = 24 8 + 3 = 11Rewrite middle term: Rewrite the middle term 11x using the two numbers found in Step 2. Express 11x as 8x + 3x. The trinomial becomes 2x^2 + 8x + 3x + 12.Factor by grouping: Factor by grouping. Group the terms as follows: (2x^2 + 8x) + (3x + 12). Factor out the common factors from each group. From 2x^2 + 8x, factor out 2x to get 2x(x + 4). From 3x + 12, factor out 3 to get 3(x + 4). Now we have 2x(x + 4) + 3(x + 4).Factor out common binomial: Factor out the common binomial factor (x + 4). The factored form is (x + 4)(2x + 3).

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Factor the trinomial:

2x^(2)+11 x+12
Answer:

Factor the trinomial: $\newline$ $2 x^{2}+11 x+12$ $\newline$ Answer:

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Q. Factor the trinomial:

\newline

2 x^{2}+11 x+12

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Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the trinomial $2x^2 + 11x + 12$ . Compare $2x^2 + 11x + 12$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find product and sum: Find two numbers whose product is $a*c$ ( $2*12 = 24$ ) and whose sum is $b$ ( $11$ ). $\newline$ We need to find two numbers that multiply to $24$ and add up to $11$ . $\newline$ The numbers $8$ and $3$ satisfy these conditions because: $\newline$ $8 * 3 = 24$ $\newline$ $8 + 3 = 11$
Rewrite middle term: Rewrite the middle term $11x$ using the two numbers found in Step $2$ . $\newline$ Express $11x$ as $8x + 3x$ . $\newline$ The trinomial becomes $2x^2 + 8x + 3x + 12$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms as follows: $(2x^2 + 8x) + (3x + 12)$ . $\newline$ Factor out the common factors from each group. $\newline$ From $2x^2 + 8x$ , factor out $2x$ to get $2x(x + 4)$ . $\newline$ From $3x + 12$ , factor out $3$ to get $3(x + 4)$ . $\newline$ Now we have $2x(x + 4) + 3(x + 4)$ .
Factor out common binomial: Factor out the common binomial factor $(x + 4)$ . $\newline$ The factored form is $(x + 4)(2x + 3)$ .