A maths - Polynomials

bonkysleuth SG

Find the values of the unknown constants for each identity (referring to A,B and C not X)

x^3 + 3x^2 - 2x + 16 = Ax^2 (x-1) + B(x-2)^2(x-1) + C(x+2)

To find C, let x =1

18 = 3C

C = 6

I'm not able to find A and B. Can anyone help? Thanks.

weewee SG

Let x = 2 to find A. Then let x = 0 to find B using the fact that c = 6.

Alternatively, expand out the terms and compare the coefficients.

bonkysleuth SG

Let x = 2 to find A. Then let x = 0 to find B using the fact that c = 6.

Alternatively, expand out the terms and compare the coefficients.

But lets say we apply your method to the question, you'll get

x^3 + 3x^2 - 2x +16 = 4a + b

32 = 4a +b

it's still impossible to find the answer. i did try using this method earlier. but i might have overlooked some essential statements.

weewee SG

2-2=0 for the b part

Xarxos SG

If you expand it out, you'll get A*x^3-A*x^2+B*x^3-5*B*x^2+8*B*x-4*B+C*x+2*C When you collect the terms, you'll get (A+B)*x^3+(-A-5*B)*x^2+(8*B+C)*x+(-4*B+2*C) Compare it to: x^3 + 3x^2 - 2x + 16 A+B = 1, -A-5*B = 3 8*B+C = -2 -4*B+2*C = 16 Just do some gaussian elimination and you're done. A = 2 B = -1 C = 6 There is an easier and quicker way to do this.. but it requires more thinking on your part.