Factor completely. 5x^(2)+22 x+21 Answer:

Identify a, b, c: Identify a, b, and c in the quadratic expression 5x^2 + 22x + 21. Compare 5x^2 + 22x + 21 with ax^2 + bx + c. a = 5 b = 22 c = 21Find two numbers: Find two numbers whose product is a*c (5*21 = 105) and whose sum is b (22). We need to find two numbers that multiply to 105 and add up to 22. The numbers 15 and 7 satisfy these conditions because: 15 * 7 = 105 15 + 7 = 22Rewrite middle term: Rewrite the middle term (22x) using the two numbers found in Step 2. 5x^2 + 22x + 21 can be rewritten as 5x^2 + 15x + 7x + 21.Factor by grouping: Factor by grouping. Group the terms: (5x^2 + 15x) + (7x + 21). Factor out the common factors from each group: 5x(x + 3) + 7(x + 3).Factor out common binomial: Factor out the common binomial factor (x + 3). The factored form is (5x + 7)(x + 3).

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Q. Factor completely.

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5 x^{2}+22 x+21

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Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $5x^2 + 22x + 21$ . Compare $5x^2 + 22x + 21$ with $ax^2 + bx + c$ . $a = 5$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $5*21 = 105$ ) and whose sum is $b$ ( $22$ ). $\newline$ We need to find two numbers that multiply to $105$ and add up to $22$ . $\newline$ The numbers $15$ and $7$ satisfy these conditions because: $\newline$ $15 * 7 = 105$ $\newline$ $15 + 7 = 22$
Rewrite middle term: Rewrite the middle term $22x$ using the two numbers found in Step $2$ . $5x^2 + 22x + 21$ can be rewritten as $5x^2 + 15x + 7x + 21$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms: $(5x^2 + 15x) + (7x + 21)$ . $\newline$ Factor out the common factors from each group: $\newline$ $5x(x + 3) + 7(x + 3)$ .
Factor out common binomial: Factor out the common binomial factor $(x + 3)$ . The factored form is $(5x + 7)(x + 3)$ .