Factor as the product of two binomials. x^(2)+3x+2=

Identify Structure: Identify the structure of the quadratic expression. The given quadratic expression is in the form x^2 + bx + c, where b = 3 and c = 2.Find Numbers: Look for two numbers that multiply to c (which is 2) and add up to b (which is 3). We need to find two numbers that multiply to give 2 and add up to give 3. The numbers 1 and 2 satisfy these conditions because 1 * 2 = 2 and 1 + 2 = 3.Write as Binomials: Write the quadratic expression as the product of two binomials using the numbers found in Step 2. The quadratic expression x^2 + 3x + 2 can be factored as (x + 1)(x + 2).Check Factorization: Check the factorization by expanding the binomials to ensure it equals the original expression. Expanding (x + 1)(x + 2) gives x^2 + 2x + x + 2, which simplifies to x^2 + 3x + 2. This matches the original expression, so the factorization is correct.

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Q. Factor as the product of two binomials.

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x^{2}+3x+2=

Identify Structure: Identify the structure of the quadratic expression. $\newline$ The given quadratic expression is in the form $x^2 + bx + c$ , where $b = 3$ and $c = 2$ .
Find Numbers: Look for two numbers that multiply to $c$ (which is $2$ ) and add up to $b$ (which is $3$ ). $\newline$ We need to find two numbers that multiply to give $2$ and add up to give $3$ . The numbers $1$ and $2$ satisfy these conditions because $1 \times 2 = 2$ and $1 + 2 = 3$ .
Write as Binomials: Write the quadratic expression as the product of two binomials using the numbers found in Step $2$ . $\newline$ The quadratic expression $x^2 + 3x + 2$ can be factored as $(x + 1)(x + 2)$ .
Check Factorization: Check the factorization by expanding the binomials to ensure it equals the original expression. $\newline$ Expanding $(x + 1)(x + 2)$ gives $x^2 + 2x + x + 2$ , which simplifies to $x^2 + 3x + 2$ . This matches the original expression, so the factorization is correct.