AshrafU
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30x^3 - 26x^2 - 48x + 8 / 3x^2 - 2x - 7} = Ax + B + (Cx+D) / 3x^2 - 2x - 7
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AshrafU
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https://www.symbolab.com/solver/step...7B2%7D-2x-7%7D



Here's a link showing the question better. I don't know how to solve for the constants.
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MathYani
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Do these things; these are hints to help you. In no particular order:
Factorise  {3x^{2}-2x-7} . Divide The numerator by the denominator. This should be enough to find constants Ax + B and the constants Cx + D is the remainder from when you divide the numerator by the denominator.

Update: Yes, person below, multiply both sides by  {3x^{2}-2x-7} because there isn't an ez way to factorise it.
Last edited by MathYani; 1 year ago
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RDKGames
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(Original post by AshrafU)
30x^3 - 26x^2 - 48x + 8 / 3x^2 - 2x - 7} = Ax + B + (Cx+D) / 3x^2 - 2x - 7
You can multiply through by the denominator and obtain that

30x^3 - 26x^2 - 48x + 8 = (Ax+B)(3x^2 -2x -7) + (Cx+D)

The value of A should be immediately obvious since the coeff of x^3 on the LHS is 30 and on the RHS it will be 3A. These must be equal.

Once you know A, you can easily work out what B is by similar style. What is the coeff of x^2 on the LHS ? What is it on the RHS?? Compare them and solve for B.

Then try to get C,D on your own.


P.S. Usually it's a good idea to factorise the denominator 3x^2-2x-7, but here you can't do that (nicely) so just follow along with what I've said.

P.S.S. You can also force the RHS into the usual expanded form by expanding it all. Then compare coeffs just by looking at the two sides. However it's useful to snipe out any constants immediately before expanding as that will make your expanding life easier with less algebra involved.
Last edited by RDKGames; 1 year ago
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AshrafU
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#5
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yess iv'e got it now. Thanks for the help.
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