express the function y = 2x³ - 11x² +17x-6 in factored form

[tex] \tt \: y = 2x {}^{3} - 11x {}^{2} + 17x - 6 \\ \\ \tt \: y = 2x {}^{3} - x {}^{2} - 10x {}^{2} + 5x + 12x - 6 \\ \\ \tt \: y = x {}^{2}(2x - 1) - 5x(2x - 1) + 6(2x - 1) \\ \\ \tt \: y = (2x - 1)(x {}^{2} - 5x + 6) \\ \\ \tt \: y = (2x - 1)(x {}^{2} - 2x - 3x + 6) \\ \\ \tt \: y = (2x - 1)(x(x - 2) - 3(x - 2)) \\ \\ \tt \orange{y = (2x - 1)(x - 2)(x - 3)}[/tex]

Therefore, (2x - 1)(x - 2)(x - 3) is the factored form of the function.

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CloudyClothyviz CloudyClothyviz · Answer 2

FUNCTION IN FACTORED FORM

Answer:

(2x - 1)(x - 2)(x - 3)

Step-by-step explanation:

Since in the given direction or sentence, we factor the function y = 2x³ - 11x² + 17x - 6.

[tex] \: \: \: \: \: \: \: \sf \: y =2{x}^{3} - 11{x}^{2} +17x-6 \\ \: \: \: \: \: \: \: \: \sf \: y = 2{x}^{3} + 11{x}^{2} +17x + 6 \\ \: \: \: \: \: \: \: \: \sf \: y = 2{x}^{3} + {x}^{2} + 10 {x}^{2} - 17x + 6 \\ \: \: \: \: \: \: \: \sf \: y = 2{x}^{3} + {x}^{2} +10 {x}^{2} - 5x - 12x + 6 \\ \sf \: \: \: \: \: {x}^{2} (2x - 1) + 10 {x}^{2} - 5x - 12x + 6 \\ \: \sf \: \: \: \: \: {x}^{2} (2x - 1) + 5x( 2x - 1) - 12x + 6 \\ \sf \: {x}^{2} (2x - 1) + 5x( 2x - 1) - 6(2x - 1) \\ \sf \: (2x - 1)( {x}^{2} - 5x + 6) \\ \sf \: (2x - 1)( {x}^{2} -2x - 3x + 6) \\ \sf \: (2x - 1)( x(x - 2) - 3x + 6) \\ \sf \: (2x - 1)( x(x - 2) - 3(x - 2)) \\ \sf \red{ = \: (2x - 1)(x - 2)(x - 3)}[/tex]

Sana tama haha. Now ko lang ito pinag-aralan. I hope my answer is helpful to you!

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