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Polynomial Arithmetic

From profit/cost models to the flight of a baseball to approximating the motion of a wave, polynomials are a mathematical way to represent values which are sums of powers of variables.

Multiplying Polynomials

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

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

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

The following polynomial in \(x\) has a coefficient of \(2\) for the quartic (degree four) term: \[(3x^4+x^3-19x^2+5x-2k)(x^4+2x^3+3x+k),\] where \(k\) is a constant. What is the constant term of the polynomial?

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

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