Factor the quadratic expression completely. 8x^(2)-18 x-5=

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Factor the quadratic expression completely.  8x^(2)-18 x-5=

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Identify Coefficients: Step Title: Identify the Coefficients Concise Step Description: Identify the coefficients of the quadratic expression, which are the numbers in front of the variables. In this case, the coefficients are 8, -18, and -5. Step Calculation: Coefficients are 8, -18, -5 Step Output: Coefficients: 8, -18, -5Find Product and Sum: Step Title: Find the Product and Sum Concise Step Description: Find two numbers that multiply to the product of the first and last coefficients (8 * -5 = -40) and add to the middle coefficient (-18). Step Calculation: We need to find two numbers that multiply to -40 and add to -18. Step Output: After testing different combinations, we find that -20 and +2 multiply to -40 and add to -18.Rewrite Middle Term: Step Title: Rewrite the Middle Term Concise Step Description: Rewrite the middle term of the quadratic expression using the two numbers found in the previous step. Step Calculation: Rewrite -18x as -20x + 2x. Step Output: The expression becomes 8x^2 - 20x + 2x - 5.Factor by Grouping: Step Title: Factor by Grouping Concise Step Description: Group the terms into two pairs and factor out the greatest common factor from each pair. Step Calculation: Factor out 4x from the first pair and 1 (or just factor the sign) from the second pair. Step Output: The expression becomes 4x(2x - 5) + 1(2x - 5).Factor Out Common Binomial: Step Title: Factor Out the Common Binomial Concise Step Description: Factor out the common binomial factor from the two groups. Step Calculation: The common binomial factor is (2x - 5). Step Output: The factored form is (2x - 5)(4x + 1).

Factor the quadratic expression completely. $\newline$ $8x^{2}-18x-5=$

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Factor the quadratic expression completely.\newline8x2−18x−5=8x^{2}-18x-5=8x2−18x−5=

Factor the quadratic expression completely. $\newline$ $8x^{2}-18x-5=$