1/28 Quiz - Unit 5 - Polynomials

Choose the expression below that is correctly represented in Standard Form.

•  $12-3x^2+24x^3-6x^4$  

•  $-6x^4+3x^3-x^5+1$  

•  $3x^6-5x^4+x-3$  

•  $x^1+x^2+x^3+x^4$  

Answer explanation

When exponents are in descending order (highest to lowest), an expression is considered to be in standard form.  It is fine if the exponents are not consecutive, but they do need to be in standard form.  For example:
 $3x^6-5x^4+x-3$  

Which of the following is an example of a quintic trinomial?

•  $x^5+4x^4+6x^3+3x^3+x^2-2$  

•  $-6x^5-3x^2-x$  

•  $-5x^4+3x-2$  

•  $3x^5$  

Answer explanation

A degree 5 polynomial (meaning that the highest exponent in the expression is a 5) is classified as 'quintic'.  A TRInomial is an expression with three terms.   Therefore the correct answer is:
 $-6x^5-3x^2-x$  

Choose the option below that correctly represents the Quotient Rule:

•  $x^7\cdot x^2=x^9$  

•  $\left(x^2\right)^7=x^{14}$  

•  $\frac{x^7}{x^2}=x^5$  

•  $x^{-2}=\frac{1}{x^2}$  

Answer explanation

While all of these correctly represent our exponent rules, only the equation below represents the quotient rule:
 $\frac{x^7}{x^2}=x^5$  

Tags

CCSS.HSA.APR.A.1

Simplify the expression below:

 $\frac{12x^5-3x^{ }}{3x}$  

•  $4x^4$  

•  $\frac{4x^4-1}{3x}$  

•  $4x^4-1$  

•  $3x^3$  

Answer explanation

Since  $12x^5$  and  $3x$  do not have the same exponent and are not considered like terms, you can not subtract in the numerator.  Therefore, you divide each term by the denominator and calculate the answer as:
 $4x^4-1$  .  Do not forget that any number over itself equals 1.  Therefore  $\frac{-3x}{3x}=-1$  

Tags

CCSS.HSA.APR.D.6

Simplify:

 $\left(8x^3-6x^4+3\right)-\left(3x^3-3+8x^4\right)\$  

•  $5x^3+3x^4-5x^4$  

•  $2x^4-8x^3$  

•  $-14x^4+11x^3-6$  

•  $-14x^4+5x^3+6$  

Answer explanation

First, distribute that negative to the second expression and you have  $-3x^3+3-8x^4$ .  Now combine like terms with the first expression and your final answer is:
 $-14x^4+5x^3+6$  

Tags

CCSS.HSA.APR.A.1

The graph represents the equation

 $f\left(x\right)=4x^4+6x^3-x$ .  You may use Desmos.com to help you determine which of the following are correct:

•  $as\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$  
   $as\ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow\ -\infty$  
  

•  $as\ x\ \rightarrow\ \infty,\ f\left(x\right)\ \rightarrow\infty$  
   $as\ x\ \rightarrow\ -\infty,\ f\left(x\right)\ \rightarrow\ \infty$  
  

•  $as\ x\ \rightarrow\ \infty,\ f\left(x\right)\ \rightarrow\ -\infty$   $as\ x\ \rightarrow\ -\infty,\ f\left(x\right)\ \rightarrow\ -\infty$  
  

•  $as\ x\ \rightarrow\ \infty,\ f\left(x\right)\ \rightarrow\ -\infty$  
   $as\ x\ \rightarrow\ -\infty,\ f\left(x\right)\ \rightarrow\ \infty$  
  

If the turning point is higher than any nearby point, it is called a

• Relative minimum

• Relative maximum

• Odd degree polynomial

• Even degree polynomial

Answer explanation

If a turning point is higher than any nearby point, it is called a relative maximum. If a turning point is lower than any nearby point, it is called a relative minimum. Maximum and minimum values are called Extrema.

Choose the correct domain and range for this graph, which represents the equation  $f\left(x\right)\ =\ x^{3\ }+6x^{2\ }+8x$  :

• Domain - All Real Numbers

  Range - All Real Number

• Domain - {y|y > 3}
  Range - {x|x > 3}

• Domain - {x|x > 3}
  Range - {y|y > 3}

• Domain - undefined
  Range - All real numbers

Answer explanation

Taking a look at the graph, and knowing that the graph will go on into infinity, it can be expected that both the domain and range include all real numbers.  You may plot this on desmos.com and take a closer look. 

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

This graph represents the equation $f\left(x\right)\ =\ x^{3\ }+6x^2+8x$  .  Which of the following correctly identifies the zeros?

• x = {-4,-2,0}

• y = {-4,-2,0}

• x = {-4,-2}

• x = {4,2}

Answer explanation

Looking at the graph, we see that the equation touches the x-axis, where y=0, at the points (-4,0), (-2,0) and the origin.  This means that our zeros (also called roots, solutions and x-intercepts) are x = {-4,-2,0}. 

Tags

CCSS.HSF-IF.C.7C

Simplify the following: $\left(4x^5\right)^3$  

•  $64x^{15}$  

•  $64x^8$  

•  $5x^8$  

•  $5x^{15}$  

Answer explanation

The power rule for exponents tells us that when you have a power to a power, you multiply those exponents. Shown as: 
 $\left(a^m\right)^n=a^{m\cdot n}$  , therefore the new exponent is  $\left(x^5\right)^3=x^{5\cdot3}=x^{15.}$ .  Note though that the 4 is also in parenthesis and therefore must be cubed as well.  $\left(4\right)^3=64.$  Final answer  $64x^{15}$  .

Tags

CCSS.HSA.APR.A.1