Factor completely. 3x^(2)+20 x+25 Answer:

Identify a, b, c: Identify a, b, and c in the quadratic expression 3x^2 + 20x + 25. Compare 3x^2 + 20x + 25 with ax^2 + bx + c. a = 3 b = 20 c = 25Find two numbers: Find two numbers whose product is a*c (3*25 = 75) and whose sum is b (20). We need to find two numbers that multiply to 75 and add up to 20. 15 * 5 = 75 15 + 5 = 20 Two numbers: 15, 5Rewrite middle term: Rewrite the middle term (20x) using the two numbers found in Step 2. 3x^2 + 15x + 5x + 25Factor by grouping: Factor by grouping. Group the terms: (3x^2 + 15x) + (5x + 25) Factor out the common factors from each group. 3x(x + 5) + 5(x + 5)Factor out common binomial: Factor out the common binomial factor (x + 5). (3x + 5)(x + 5)

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Q. Factor completely.

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3 x^{2}+20 x+25

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Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3x^2 + 20x + 25$ . Compare $3x^2 + 20x + 25$ with $ax^2 + bx + c$ . $a = 3$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $3*25 = 75$ ) and whose sum is $b$ ( $20$ ). $\newline$ We need to find two numbers that multiply to $75$ and add up to $20$ . $\newline$ $15 * 5 = 75$ $\newline$ $15 + 5 = 20$ $\newline$ Two numbers: $15, 5$
Rewrite middle term: Rewrite the middle term $20x$ using the two numbers found in Step $2$ . $3x^2 + 15x + 5x + 25$
Factor by grouping: Factor by grouping. $\newline$ Group the terms: $(3x^2 + 15x) + (5x + 25)$ $\newline$ Factor out the common factors from each group. $\newline$ $3x(x + 5) + 5(x + 5)$
Factor out common binomial: Factor out the common binomial factor $(x + 5)$ . $\newline$ $(3x + 5)(x + 5)$