Factor completely. 2x^(2)+24 x+22 Answer:

Write Quadratic Expression: Write down the quadratic expression that needs to be factored. The given quadratic expression is 2x^(2)+24x+22.Find Greatest Common Factor: Look for a greatest common factor (GCF) that can be factored out from all the terms in the quadratic expression. The GCF of 2x^(2), 24x, and 22 is 2.Factor Out GCF: Factor out the GCF from the quadratic expression. 2x^(2)+24x+22 = 2(x^(2)+12x+11)Factor Quadratic Expression: Now, we need to factor the quadratic expression inside the parentheses, x^(2)+12x+11. We are looking for two numbers that multiply to 11 (the constant term) and add up to 12 (the coefficient of the x term). The numbers that satisfy these conditions are 1 and 11.Use Two Numbers: Write the factored form of the quadratic expression using the two numbers found in Step 4. 2(x^(2)+12x+11) = 2(x+1)(x+11)Write Factored Form: Check the factored expression by expanding it to ensure it matches the original expression. 2(x+1)(x+11) = 2(x^2 + 11x + x + 11) = 2(x^2 + 12x + 11) = 2x^2 + 24x + 22 This matches the original expression, so the factorization is correct.

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Factor completely.

2x^(2)+24 x+22
Answer:

Factor completely. $\newline$ $2 x^{2}+24 x+22$ $\newline$ Answer:

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Q. Factor completely.

\newline

2 x^{2}+24 x+22

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Answer:

Write Quadratic Expression: Write down the quadratic expression that needs to be factored. $\newline$ The given quadratic expression is $2x^{2}+24x+22$ .
Find Greatest Common Factor: Look for a greatest common factor (GCF) that can be factored out from all the terms in the quadratic expression. $\newline$ The GCF of $2x^{2}$ , $24x$ , and $22$ is $2$ .
Factor Out GCF: Factor out the GCF from the quadratic expression. $\newline$ $2x^{2}+24x+22 = 2(x^{2}+12x+11)$
Factor Quadratic Expression: Now, we need to factor the quadratic expression inside the parentheses, $x^{2}+12x+11$ . We are looking for two numbers that multiply to $11$ (the constant term) and add up to $12$ (the coefficient of the $x$ term). The numbers that satisfy these conditions are $1$ and $11$ .
Use Two Numbers: Write the factored form of the quadratic expression using the two numbers found in Step $4$ . $\newline$ $2(x^{2}+12x+11) = 2(x+1)(x+11)$
Write Factored Form: Check the factored expression by expanding it to ensure it matches the original expression. $\newline$ $2(x+1)(x+11) = 2(x^2 + 11x + x + 11) = 2(x^2 + 12x + 11) = 2x^2 + 24x + 22$ $\newline$ This matches the original expression, so the factorization is correct.