Polynomial Arithmetic

Multiplying Polynomials


Which of the following is the correct expansion of (x+4)(x2+3)? (x+4)(x^2+3) ?

What is the sum of all the coefficients in the expansion of the expression (x2y)(9x6y8)?(x-2y)(9x-6y-8)?

If the expansion of (x+114y)(x115y)\left(x+\frac{1}{14}y\right)\left(x-\frac{1}{15}y\right) gives x2+axy+by2,x^2+axy+by^2, where aa and bb are constants, what is ab?\frac{a}{b}?

The following polynomial in xx has a coefficient of 22 for the quartic (degree four) term: (3x4+x319x2+5x2k)(x4+2x3+3x+k),(3x^4+x^3-19x^2+5x-2k)(x^4+2x^3+3x+k), where kk is a constant. What is the constant term of the polynomial?

If the expansion of (x+2y)(Ax+9y)(x+2y)(Ax+9y) gives 3x2+Bxy+18y2,3x^2+Bxy+18y^2, where AA and BB are constants, what is A+B?A+B?


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