Polynomials and Division

The function  $g\left(x\right)=2x^3+8x^2-22x\ -60$  can be written in factored form. Which factored for equation is equivalent to g(x).

•  $g\left(x\right)=2\left(x+3\right)\left(x-5\right)\left(x+2\right)$  

•  $g\left(x\right)=2\left(x+3\right)\left(x-5\right)\left(x-2\right)$  

•  $g\left(x\right)=2\left(x-3\right)\left(x+5\right)\left(x+2\right)$  

•  $g\left(x\right)=2\left(x-3\right)\left(x-5\right)\left(x+2\right)$  

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Which of the following general form equations in equivalent to the function  $g\left(x\right)=3\left(x-5\right)\left(x+7\right)\left(x+3\right)^2$  ?

•  $g\left(x\right)=3x^4+24x^3-42x^2-576x-945$  

•  $g\left(x\right)=3x^4-5x^3+7x^2+3x+3$  

•  $g\left(x\right)=3x^{4\ }+24x^3+42x^2+576x-945$  

•  $g\left(x\right)=\ 3x^4+5x^3-7x^2-3x-3$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Given the following graph which of the following statements is true. Check all that apply.

• The x-intercept x=1 has a multiplicity of three, the x-intercept x=-2 has a multiplicity of three

• The x-intercept x=1 has a multiplicty of two, the x-intercept x=-2 has a mulitplicity of three

• A fifth degree polynomial is the smallest degree polynomial that can be used to model the graph.

• The polynomial has a odd exponent and a positive leading coefficient.

Given the following graph which of the following statements is true. Check all that apply.

• There are three real zeros and zero complex/imaginary zeros

• The lowest possible degree polynomial that can be used to model the graph is a 6th degree polynomial

• The x-intercept x=3 has a multiplicity of 3, the x-intercept of x =-1 has a multiplicity of one, the x-intercept of x=-2 has a multiplicity of one.

• The graph has two relative minimums (-2,0) and approximately (0.75,-38)

Tags

CCSS.HSA.APR.B.3

Given the polynomial  $h\left(x\right)=-2x^3-10x^2+5x\ -43$  determine the relative minimum and relative maximum.

• Relative minimum (-3.57, -97.3) Relative maximum ( 0.234, -42.4)

• Relative minimum (-6.01, 0)  Relative maximum (0, -43)

• Relative minimum (0.234, -42.4) Relative Maximum (-3.57, -97.3)

• Relative Minimum (0,-43) Relative Maximum (-6.01, 0 )

Given the polynomial  $f\left(x\right)=-2x^3-10x^2+5x\ -43$  , which statements regarding the polynomials end behavior are true?

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

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

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

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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which statements describe the end behavior to the given polynomial?

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

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

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

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

• x=-4 is a triple root, x=3 is a double root

  x=-2 is a single root

• x=-4 is a double root, x=3 is a triple root, x=-2 is a single root

• x=-4 is a triple root, x=3 is a single root, x=-2 is a double root

• x=-4 is a single root, x=3 is a double root, x=-2 is a single root

Which of the following equations meet the following criteria. Has one x-intercept with a multiplicity of 2, and one that has a multiplicity of 3, and is degree 6.

• $f\left(x\right)=\left(x-2\right)\left(x+3\right)^3\left(x-1\right)^2$

• $i\left(x\right)=x^6-22x^5+177x^4-576x^3+216x^2+2592x-3888$

• $g\left(x\right)=\left(x-2\right)\left(x+3\right)^2\left(x-4\right)^3\left(x-5\right)$

• $g\left(x\right)=x^6-5x^3+3x^2-2x-3$

Tags

CCSS.HSA.APR.B.3

Given the functions  $p\left(x\right)=\ 2x^3-5x^2-3x+7$  and  $h\left(x\right)=2\left(1.25\right)^x$  . When is  $p\left(x\right)>h\left(x\right)$  ?

•  $\left(-1.102,.804\right)U\left(2.828,\ \infty\right)$  

•  $\left(-\infty,-1.210\right)U\left(.804,2.828\right)$  

•  $\left(-\infty,\infty\right)$  

•  $\left(-\infty,-1.102\right)U\left(2.828,\infty\right)$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.D.11

CCSS.HSF.LE.A.3