Posted by Jay on Monday, June 6, 2011 at 10:58pm.
Can somebody explain to me why equating coefficients work?
8x^3+13x = Ax^3 + 2Ax + Bx^2 + 2B + Cx + D
8x^3 + 13x = Ax^3 + Bx^2 + (2A+C)x + 2(B+D)
where A,B,C,D are constants.
Why does 8 = A; 0 = B; 13 = 2A + C; etc.
I know they have same power variables, but why does this actually work? Thanks!
- calculus(equating coefficients) - MathMate, Tuesday, June 7, 2011 at 12:20am
8x^3+13x ≡ Ax^3 + 2Ax + Bx^2 + 2B + Cx + D ...(1)
(8-A)x^3-Bx²+(13-2A-C)x -(2B+C)≡ 0 ...(2)
This is an identity, and has to work for all values of x.
This can happen if and only if the coefficients on the left-hand side of (2) are zero, which then implies
8-A=0, or A=8,
Answer This Question
More Related Questions
- Calculus 2 - use the method of equating coefficients. integral of (x^3+5x^2+12...
- algebra - Could somebody tell me in simple terms why equating coefficients works...
- Algebra - Divide... 1. x^3+2x^2+x+12/x+3 2. 45a^6b^10/5a^3b^2 Note that x^3+2x^2...
- math/algebra - subtract. express in simplest form 13x/30 - 4x/ 15 = factor the ...
- Math - Factor into polynomials with integral coefficients: 6x^2+13x+6
- algebra 2 - factor completely 3x^2-14x-24 I do not see the gcf for the problem I...
- Algebra - Can you pleas Solve the quadric equation step by step 4x square =13x+...
- Algebra - Hello all - I would like to check my work on 2 problems. Solve by ...
- intermidate algebra - Solve each equadratic equation by factoring. 6^2-13x-28 36...
- intermidate algebra - 6^2-13x=-5 6^2-13x=-5 6^2=13x-5 I have tried this problem ...