11x²-198x-120

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11x²-198x-120

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Identify Quadratic Trinomial: Identify the quadratic trinomial and check if there is a common factor for all terms. 11x²-198x-120 Check for common factors: GCD(11, 198, 120) = 11Factor Out GCD: Factor out the greatest common divisor (GCD) from the quadratic trinomial. 11(x²-18x-11)Find Two Numbers: Now, we need to factor the quadratic expression inside the parentheses. Look for two numbers that multiply to -11 (the product of the coefficient of x² and the constant term) and add up to -18 (the coefficient of x). The numbers that satisfy these conditions are -22 and +1.Rewrite Middle Term: Rewrite the middle term -18x using the two numbers found in the previous step. 11(x²-22x+x-11)Group and Factor: Group the terms in pairs and factor by grouping. 11((x²-22x)+(x-11))Factor Common Factors: Factor out the common factors from each group. 11(x(x-22)+1(x-11))Re-evaluate Factors: Notice that (x-22) and (x-11) are not common factors, and we cannot factor further. This indicates a mistake was made in the previous steps because the quadratic should be factorable. We need to re-evaluate the factors of -11 that add up to -18.

$11x^2-198x-120$

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$11x^2-198x-120$