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- Operations - Multiplication & Division

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**Multiplication: ** To multiply two polynomials we use the laws of exponents in conjunction with the distributive law. $$(ax + b) * ( cx + d) =$$ $$ac x^2 + adx + bcx + bd =$$ $$ac x^2 + ( ad + bc) x + bd$$

**Division:** If f(x) and d(x)are polynomials, and the degree of d(x) is less than or equal to the degree of f(x), then there exist unique polynomials q(x) and r(x), such that

and the degree of r(x) is **less than** the degree of d(x).

In the special case where r(x) = 0, we say that d(x) **divides evenly** into f(x).

The expression q(x) is called the **quotient**, and the expression d(x) is called the **divisor** and the r(x) is called **remainder**.

Multiplication $$(4x + 7) × ( 2x + 3) =$$ $$8 x^2 + 12x + 14x + 21 =$$ $$8 x^2 + ( 12 + 14) x + 21$$

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