Factor completely. 3x^(2)+10 x+3 Answer:

Identify a, b, c: Identify a, b, and c in the quadratic expression 3x^2 + 10x + 3. Compare 3x^2 + 10x + 3 with ax^2 + bx + c. a = 3 b = 10 c = 3Find product and sum: Find two numbers whose product is a*c (3*3 = 9) and whose sum is b (10). We need to find two numbers that multiply to 9 and add up to 10. The numbers 1 and 9 satisfy these conditions because: 1 * 9 = 9 1 + 9 = 10Rewrite middle term: Rewrite the middle term (10x) using the two numbers found in Step 2. 3x^2 + 10x + 3 can be rewritten as: 3x^2 + 1x + 9x + 3Factor by grouping: Factor by grouping. Group the terms into two pairs: (3x^2 + 1x) + (9x + 3) Factor out the greatest common factor from each pair: x(3x + 1) + 3(3x + 1)Factor out common binomial: Factor out the common binomial factor. Both groups contain the common binomial factor (3x + 1), so factor this out: (3x + 1)(x + 3)

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Q. Factor completely.

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3 x^{2}+10 x+3

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Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3x^2 + 10x + 3$ . Compare $3x^2 + 10x + 3$ with $ax^2 + bx + c$ . $a = 3$ $b$ $0$ $b$ $1$
Find product and sum: Find two numbers whose product is $a*c$ ( $3*3 = 9$ ) and whose sum is $b$ ( $10$ ). $\newline$ We need to find two numbers that multiply to $9$ and add up to $10$ . $\newline$ The numbers $1$ and $9$ satisfy these conditions because: $\newline$ $1 * 9 = 9$ $\newline$ $1 + 9 = 10$
Rewrite middle term: Rewrite the middle term $10x$ using the two numbers found in Step $2$ . $3x^2 + 10x + 3$ can be rewritten as: $3x^2 + 1x + 9x + 3$
Factor by grouping: Factor by grouping. $\newline$ Group the terms into two pairs: $\newline$ $(3x^2 + 1x) + (9x + 3)$ $\newline$ Factor out the greatest common factor from each pair: $\newline$ $x(3x + 1) + 3(3x + 1)$
Factor out common binomial: Factor out the common binomial factor. $\newline$ Both groups contain the common binomial factor $(3x + 1)$ , so factor this out: $\newline$ $(3x + 1)(x + 3)$