## Section11.6Additional Practice Related to Polynomials

### ExercisesExercises

Questions vary.

###### 1.

Identify the degree, the leading term, the leading coefficient, the linear term(s), and the constant term for the following polynomial.

\begin{equation*} -2+8x+4x^3-x^4 \end{equation*}
Solution

The degree is $4\text{,}$ the leading term is $-x^4\text{,}$ the leading coefficient is $-1\text{,}$ the linear term is $8x\text{,}$ and the constant term is $-2\text{.}$

###### 2.

Identify the degree, the leading term, the leading coefficient, the linear term(s), and the constant term for the following polynomial.

\begin{equation*} 4x+12xy-8y \end{equation*}
Solution

The degree is $2\text{,}$ the leading term is $12xy\text{,}$ the leading coefficient is $12\text{,}$ the linear terms are $4x$ and $-8y\text{,}$ and there are no constant terms.

###### 3.

Identify each of the following as a trinomial, binomial, monomial, or not any of those type of polynomial.

\begin{equation*} 7xy \end{equation*}
\begin{equation*} 3x^3-2x^2+x-1 \end{equation*}
\begin{equation*} x^2y^2+6 \end{equation*}
\begin{equation*} -x^3+7x^2+8x \end{equation*}
Solution
\begin{equation*} 7xy\text{ is a monomial} \end{equation*}
\begin{equation*} 3x^3-2x^2+x-1\text{ is not a trinomial, binomial, or monomial} \end{equation*}
\begin{equation*} x^2y^2+6\text{ is a binomial} \end{equation*}
\begin{equation*} -x^3+7x^2+8x\text{ is a trinomial} \end{equation*}

Perform the indicated operation and simplify the result.

###### 4.

$(-3x^2+5x+4)-(-8x^2-4x+7)$

Solution

$(-3x^2+5x+4)-(-8x^2-4x+7)=5x^2+9x-3$

###### 5.

$2(x^4-3x^3+2x-4)+(6x^4-5x^2-4x+8)$

Solution

$2(x^4-3x^3+2x-4)+(6x^4-5x^2-4x+8)=8x^4-6x^3-5x^2$

###### 6.

$-(-3x^2+6x-3)-2(x^2-7x+4)$

Solution

$-(-3x^2+6x-3)-2(x^2-7x+4)=x^2+8x-5$

###### 7.

$(4x+3)(2x-9)$

Solution

$(4x+3)(2x-9)=8x^2-30x-27$

###### 8.

$(2x-9)^2$

Solution

$(2x-9)^2=4x^2-36x+81$

###### 9.

$x(x+8)(x-8)$

Solution

$x(x+8)(x-8)=x^3-64x$

###### 10.

$(-x^2y^4+2xy)(3x^2y^4-5xy)$

Solution

$(-x^2y^4+2xy)(3x^2y^4-5xy)=-3x^4y^8+11x^3y^5-10x^2y^2$

###### 11.

$(x+4)(x^2-7x+3)$

Solution

$(x+4)(x^2-7x+3)=x^3-3x^2-25x+12$

###### 12.

$(x^3+3x^2-x-4)(x-3)$

Solution

$(x^3+3x^2-x-4)(x-3)=x^4-10x^2-x+12$

###### 13.

$(y+5)^3$

Solution

$(y+5)^3=y^3+15y^2+75y+125$

###### 14.

$\frac{-3x^2+15x-3}{-3}$

Solution

$\frac{-3x^2+15x-3}{-3}=x^2-5x+1$

###### 15.

$\frac{42x^5y^8-54x^4y^6+18x^3y^4}{6xy^4}$

Solution

$\frac{42x^5y^8-54x^4y^6+18x^3y^4}{6xy^4}=7x^4y^4-9x^3y^2+3x^2$

###### 16.

$\frac{(xy+3x)(xy-3x)}{-x^2}$

Solution

$\frac{(xy+3x)(xy-3x)}{-x^2}=-y^2+9$