Factor completely. 5x^(2)+75 x+270 Answer:

Identify Terms: Identify the coefficients and constant term in the quadratic expression 5x^2 + 75x + 270. The coefficient of x^2 (a) is 5, the coefficient of x (b) is 75, and the constant term (c) is 270.Find GCF: Look for a greatest common factor (GCF) that can be factored out from all the terms in the expression. The GCF of 5, 75, and 270 is 5. Factor out the GCF from the expression: 5(x^2 + 15x + 54).Factor Out GCF: Now, focus on factoring the quadratic expression inside the parentheses: x^2 + 15x + 54. We need to find two numbers that multiply to give ac (5 * 54 = 270) and add up to b (15). The numbers that satisfy these conditions are 9 and 6, since 9 * 6 = 54 and 9 + 6 = 15.Factor Quadratic Expression: Write the factored form of the quadratic expression using the numbers found in the previous step. The factored form is 5(x + 9)(x + 6).

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Q. Factor completely.

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5 x^{2}+75 x+270

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Answer:

Identify Terms: Identify the coefficients and constant term in the quadratic expression $5x^2 + 75x + 270$ . The coefficient of $x^2$ $(a)$ is $5$ , the coefficient of $x$ $(b)$ is $75$ , and the constant term $(c)$ is $270$ .
Find GCF: Look for a greatest common factor (GCF) that can be factored out from all the terms in the expression. $\newline$ The GCF of $5$ , $75$ , and $270$ is $5$ . $\newline$ Factor out the GCF from the expression: $5(x^2 + 15x + 54)$ .
Factor Out GCF: Now, focus on factoring the quadratic expression inside the parentheses: $x^2 + 15x + 54$ . We need to find two numbers that multiply to give $ac$ ( $5 \times 54 = 270$ ) and add up to $b$ ( $15$ ). The numbers that satisfy these conditions are $9$ and $6$ , since $9 \times 6 = 54$ and $9 + 6 = 15$ .
Factor Quadratic Expression: Write the factored form of the quadratic expression using the numbers found in the previous step. $\newline$ The factored form is $5(x + 9)(x + 6)$ .