Factor. 5d^2 + 8d + 3 ______

Identify a, b, c: Identify a, b, and c in the quadratic expression 5d^2 + 8d + 3 by comparing it with the standard form ax^2 + bx + c. a = 5 b = 8 c = 3Find two numbers: Find two numbers that multiply to a*c (which is 5*3=15) and add up to b (which is 8). The two numbers that satisfy these conditions are 5 and 3 because: 5 * 3 = 15 5 + 3 = 8Rewrite middle term: Rewrite the middle term, 8d, using the two numbers found in the previous step. 5d^2 + 8d + 3 can be rewritten as: 5d^2 + 5d + 3d + 3Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together: (5d^2 + 5d) + (3d + 3)Factor out common factor: Factor out the greatest common factor from each group: 5d(d + 1) + 3(d + 1)Final factorization: Since both groups contain the common factor (d + 1), factor this out: (5d + 3)(d + 1)

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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5d^2 + 8d + 3

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $5d^2 + 8d + 3$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 5$ $\newline$ $b = 8$ $\newline$ $b$ $0$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $5*3=15$ ) and add up to $b$ (which is $8$ ). $\newline$ The two numbers that satisfy these conditions are $5$ and $3$ because: $\newline$ $5 \times 3 = 15$ $\newline$ $5 + 3 = 8$
Rewrite middle term: Rewrite the middle term, $8d$ , using the two numbers found in the previous step. $\newline$ $5d^2 + 8d + 3$ can be rewritten as: $\newline$ $5d^2 + 5d + 3d + 3$
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together: $5d^2 + 5d$ + $3d + 3$
Factor out common factor: Factor out the greatest common factor from each group: $5d(d + 1) + 3(d + 1)$
Final factorization: Since both groups contain the common factor $(d + 1)$ , factor this out: $\newline$ $(5d + 3)(d + 1)$