danaebaby11 danaebaby11
  • 23-04-2020
  • Mathematics
contestada

3x^3-2x^2-147x+98=(ax-c)(bx+d)(bx-d) where a,b,c and d positive integers. Work out the value of a,b,c and d

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LammettHash
LammettHash LammettHash
  • 24-04-2020

Expand the right side:

[tex](ax-c)(bx+d)(bx-d)=(ax-c)(b^2x^2-d^2)[/tex]

[tex]=ab^2x^3-b^2cx^2-ad^2x+cd^2[/tex]

Notice that 98 = 2 * 7 * 7, so we have [tex]c=2[/tex] and [tex]d=7[/tex].

Then

[tex]-ad^2=-147\implies a=\dfrac{147}{49}=3[/tex]

and

[tex]ab^2=3\implies b^2=1\implies b=1[/tex]

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