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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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