Factor. 2x^2 + 9x + 4 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2x^2 + 9x + 4 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 9, c = 4Find two numbers: Find two numbers that multiply to a*c (which is 2*4 = 8) and add up to b (which is 9). The numbers 1 and 8 multiply to 8 and add up to 9.Rewrite middle term: Rewrite the middle term 9x using the two numbers found in the previous step, splitting it into 8x and 1x. 2x^2 + 9x + 4 becomes 2x^2 + 8x + 1x + 4.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (2x^2 + 8x) + (1x + 4)Factor out common factor: Factor out the greatest common factor from each group. 2x(x + 4) + 1(x + 4)Final factorization: Since both groups contain the common factor (x + 4), factor it out. (2x + 1)(x + 4)

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2x^2 + 9x + 4

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2x^2 + 9x + 4$ by comparing it to the standard form $ax^2 + bx + c$ . $\newline$ $a = 2$ , $b = 9$ , $c = 4$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $2*4 = 8$ ) and add up to $b$ (which is $9$ ). $\newline$ The numbers $1$ and $8$ multiply to $8$ and add up to $9$ .
Rewrite middle term: Rewrite the middle term $9x$ using the two numbers found in the previous step, splitting it into $8x$ and $1x$ . $\newline$ $2x^2 + 9x + 4$ becomes $2x^2 + 8x + 1x + 4$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(2x^2 + 8x) + (1x + 4)$
Factor out common factor: Factor out the greatest common factor from each group. $2x(x + 4) + 1(x + 4)$
Final factorization: Since both groups contain the common factor $(x + 4)$ , factor it out. $(2x + 1)(x + 4)$