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Question 28946: How do I add polynomials?
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! How do I add polynomials?
Linear functions of the form (ax+b) where a and b are constants
And quadratic funcitons of the form (ax^2+bx+c) where a,b and c are constants
ARE special cases of polynomials.
A polynomial function is a function of the form
f(x) = A(x^n) +B[x^(n-1)]+ C[x^(n-2)]+ ......+Lx + T where
A,B,C,....L and T are constants called the coefficients.
Here n is a non negative integer and if the coefficient A of the highest power term (here the highest power is n) is NOT ZERO ,we say that f(x) is a polynomial of degree n and A is called the leading coefficient.
Now let us consider two polynomial f(x) say of degree n and g(x) of degree m
with n>m say
f(x)=A(x^n)+B[x^(n-1)]+ C[x^(n-2)]+....+ H[x^(m+1)]+U[x^m]+V[x^(m-1)]..+Lx + T
----(1)
g(x) = A'(x^m) +B'[x^(m-1)]+ C'[x^(m-2)]+ ......+L'x + T' ----(2)
Then f(x) +g(x) is also a polynomial and is got by adding the terms of like powers of x.
Please try to follow the numerical example that is given at the end and then try to see the meaning in the theoretical definiton.
[f(x)+g(x)] = {A(x^n)+B[x^(n-1)]+ C[x^(n-2)]+....+ H[x^(m+1)]}
+{(U+A')[x^m]+(V+B')[x^(m-1)]+.....+(L+L')x+(T+T')}
Very confusing?!!.
Don't worry!. Have the above format and study it with the help of the following example. In fact it is these examples you are going to come across very often in your problems.So long as it is smooth sailing then there is no worry.Otherwise you will have to fall back on the theory which can never fail!
f(x)= 4x^9 -7x^8+11x^7 +13x^6-3x^5+19x^4-10x^3+12x^2+15x-21 ----(1)
g(x) = 5x^6+17x^5-14x^4-13x^3+x^2+x+50 ----(2)
Then f(x)+g(x)= 4x^9 -7x^8+11x^7 +(13+5)x^6+(-3+17)x^5+(19-14)x^4+(-10-13)x^3
+(12+1)x^2+(15+1)x+(-21+50)
=4x^9 -7x^8+11x^7 +18x^6+14x^5+5x^4-23x^3+13x^2+16x+29
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