1.4 Polynomials  (Page 2/15)

1. The highest power of x is 3, so the degree is 3. The leading term is the term containing that degree, $\mathrm{-4}{x}^3.$ The leading coefficient is the coefficient of that term, $\mathrm{-4.}$
2. The highest power of t is $5,$ so the degree is $5.$ The leading term is the term containing that degree, $5t^5.$ The leading coefficient is the coefficient of that term, $5.$
3. The highest power of p is $3,$ so the degree is $3.$ The leading term is the term containing that degree, $-p^3,$ The leading coefficient is the coefficient of that term, $\mathrm{-1.}$

$$\begin{array}{cc}4x^3+\left(12x^2+8x^2\right)+(9x-5x)+(\mathrm{-21}+20) \hfill & \text{Combine like terms}.\hfill \\ 4x^3+20x^2+4x-1\hfill & \text{Simplify}.\hfill \end{array}$$

$$\begin{array}{cc}7x^4-5x^3+\left(-x^2+2x^2\right)+(6x-3x)+(1-2)\hfill & \text{Combine like terms}.\hfill \\ 7x^4-5x^3+x^2+3x-1\hfill & \text{Simplify}.\hfill \end{array}$$

$$\begin{array}{cc}2x\left(3x^2-x+4\right)+1\left(3x^2-x+4\right) \hfill & \text{Use the distributive property}.\hfill \\ \left(6x^3-2x^2+8x\right)+\left(3x^2-x+4\right)\hfill & \text{Multiply}.\hfill \\ 6x^3+\left(\mathrm{-2}{x}^2+3x^2\right)+(8x-x)+4\hfill & \text{Combine like terms}.\hfill \\ 6x^3+x^2+7x+4 \hfill & \text{Simplify}.\hfill \end{array}$$