Module C Outcome 8 Polynomial Division

Given

 $h\left(x\right)=\ x^3-4x^2+7x-28$  and  $m\left(x\right)=x^2+7$  Check all that apply.

• The quotient of  $\frac{h\left(x\right)}{m\left(x\right)}$  is  x - 4

•  $m\left(x\right)\$  is a factor of   $h\left(x\right)$  because the remainder is 0

•  $m\left(x\right)\$  is not a factor of  $h\left(x\right)$  because the remainder is not 0

• The quotient if  $\frac{h\left(x\right)}{m\left(x\right)}$  is  $x-4\ +\frac{-7}{x^2+7}$  

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.D.6

 $g\left(x\right)=x^{3\ }-729$  

Check all that apply regarding the function g(x).

• g(x) factors to  $\left(x-9\right)\left(x^2+9x+81\right)$  

• g(x) factors to  $\left(x-9\right)\left(x^2-9x+81\right)$  

• g(x) has one real zeros and 2 imaginary complex roots

• g(x) has 3 real zeros

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

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

 $k\left(x\right)\ =\ x^3+1331$  

Given the cubic function, check all that apply.

• k(x) factors to  $\left(x-11\right)\left(x^2-11x+121\right)$  

• k(x) factors to  $\left(x-11\right)\left(x^2+11x+121\right)$  

• k(x) factors to  $\left(x+11\right)\left(x^2+11x+121\right)$  

• k(x) has one real x-intercepts and 2 imaginary complex x-intercepts

• A factor of k(x) is (x+11)

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

Given  $h\left(x\right)=\ x^3-kx^2+8x+4\$  and  $m\left(x\right)=x-3$  what is the value of k if the remainder of  $\frac{h\left(x\right)}{m\left(x\right)}$  is 10.

• k = 4

• k = -4

• k = 5

• k = -5

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.D.6

Given $n\left(x\right)=x^5-3x^4+x^3+x^2+4$  check all that apply

• n(x) is a a 5th degree polynomial that has two real zeros at 2 and -1, and has two complex imaginary roots

• The x-intercept of 2 on n(x) has a multiplicity of 3

• n(x) can be be written in factors  $n\left(x\right)=\ \left(x^2+1\right)\left(x-2\right)^2\left(x+1\right)$  

• n(x) can be written in factors  $n\left(x\right)=\left(x^2-1\right)\left(x-2\right)^2\left(x+1\right)$  

Tags

CCSS.HSA.APR.B.3

Given the following cubic function $d\left(x\right)=\ x^3+2x^2+2x+1$  , check all that apply

• When d(x) is divided by  $r\left(x\right)=x-1$  the remainder is 6

• When d(X) is divided by  $g\left(x\right)\ =\ x+2$  the remainder is 21

• When you divide by  $v\left(x\right)=x+1$  the remainder is 0 meaning it is a factor

• The function d(X) has 1 real root at -1 and two imaginary complex roots.

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

Jill is going to make an open top box from a 35in by 47in rectangular piece of cardboard.

What will be true about Jills open top box?

• The maximized volume of the box is approximately $4,863\ in^3$

• The maximized volume of the box is approximately $9,726\ in^3$

• The maximized dimensions of the box are 6.62 in, 21.76 in, 33.76 in

• The maximized dimensions of the box are 13.23 in, 28.38in , 40.38 in

• $v\left(x\right)\ =x^3-82x^2+1645x$

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

Abigail invests $5000 at an annual interest of 3.5% compounded monthly. Check all that apply.

• Abigail will earn $14.58 in interest after 1 month.

• It will take approximately 20 years for Abigail to double her money

• It will take approximately 19 years for Abigail to double her money

• The inverse of Abigails compound interest formula is $p^{-1}\left(x\right)=12\log_{1.0029}\left(\frac{x}{5000}\right)$

  
  

• The inverse of Abigails compound interest formula is $p^{-1}\left(x\right)=\frac{1}{12}\log_{1.0029}\left(\frac{x}{5000}\right)$

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Given the function  $c\left(x\right)=2\left(\frac{3}{5}\right)^{\left(-\frac{2}{3}x\right)}$  check all that apply

• c(x) can be rewritten as  $c\left(x\right)=2\left(1.4057\right)^x$  

• c(x) is growth and has a percent of increase of 40.57%

• c(x) can be rewritten as  $c\left(x\right)=2\left(0.711\right)^x$  

• c(x) is growth and has a percent of increase of 60%
  

• C(x) is decay and can has a percent of decrease of 28.9%

Tags

CCSS.HSF.IF.C.8

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2