Algebra

Polynomial Arithmetic

Combining Like Terms

         

What is the coefficient of x4 x^ {4} in the following polynomial:

6x4+4x3+15x4+4x15? -6 x^ {4} + 4 x^3 + 15 x^{4} + 4 x^{15} ?

After combining like terms, what is the sum of the coefficients of the xy xy and x x terms in the polynomial 3x+7xy+25y+11x3xy?3x+7xy+25y+11x-3xy?

After combining like terms, what is the sum of all coefficients of the polynomial 2x(x12y(6x5y))?2x-(x-12y-(6x-5y))?

For example, the polynomial 2x+3y+2 2x + 3y + 2 has coefficients of 2,32, 3 and 22, and the sum of all coefficients is 2+3+2=7 2 + 3 + 2 = 7 .

Rewrite the following expression in the form ax+by ax + by , and determine the sum of aa and bb: 5x(4x+3y(2xy))+63y.5x-(4x+3y-(2x-y))+63y.

Given f(x)=8x+5 f(x) = 8x + 5 and g(x)=5x+12 g(x) = 5x + 12 , what is the value of the constant term in f(x)+g(x) f(x) + g(x) ?

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