Factor completely. 3x^(2)+22 x+7 Answer:

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

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Factor completely.

3x^(2)+22 x+7
Answer:

Factor completely. $\newline$ $3 x^{2}+22 x+7$ $\newline$ Answer:

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Q. Factor completely.

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3 x^{2}+22 x+7

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Answer:

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