Verified answer

Answer:

Given down....

Step-by-step explanation:

TO FACTORIZE :

[tex]2x^{3} -3x^{2} -17x+30[/tex]

[tex]=2x^{3} +2x^{2} -5x^{2} -12x-5x+30[/tex]

[tex]=2x^{3} +2x^{2} -12x-5x^{2} -5x+30[/tex]

[tex]=2x(x^{2} +x-6) - 5(x^{2} +x-6)[/tex]

[tex]=(x^{2} +x-6)(2x-5)[/tex]

[tex]=(x^{2} +3x-2x-6)(2x-5)[/tex]

[tex]=[x(x+3)-2(x+3)](2x-5)[/tex]

[tex]=(x+3)(x-2)(2x-5)[/tex]

[tex]x^{3} -6x^{2} +11x-6[/tex]

[tex]=x^{3} -5x^{2} -x^{2} +6x+5x-6[/tex]

[tex]=x^{3} -5x^{2} +6x-x^{2} +5x-6[/tex]

[tex]=x(x^{2} -5x+6)-1(x^{2} -5x+6)[/tex]

[tex]=(x-1)(x^{2} -5x+6)[/tex]

[tex]=(x-1)(x^{2} -2x-3x+6)[/tex]

[tex]=(x-1)[x(x-2)-3(x-2)][/tex]

[tex]=(x-1)(x-2)(x-3)[/tex]

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