Unit 3 Test Study Guide

A polynomial equation has zeros at x = ±1 and x = 2i. What is the minimum degree of the polynomial equation? (assuming all coefficients are real)

• 4

• 3

• 2

• 1

Consider the graph of

 $f\left(x\right)=2x^4+4x^3-5x^2-5x+6$  shown. How many zeros of the function must be imaginary?

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• 1

• 2

• 3

Write the polynomial function of least degree that has zeros of x = 2 and x = 3i. (assume all coefficients must be real)

• $f\left(x\right)=x^3-2x^2+9x-18$

• $f\left(x\right)=x^3+2x^2+9x+18$

• $f\left(x\right)=x^2-3ix-2x-6$

• $f\left(x\right)=x^2-6x-6$

Tags

CCSS.HSA.APR.B.3

Which polynomial function graphed below has at least 4 imaginary zeros?

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Which of the below could be a correct polynomial function for the graph shown at the right based on it zeros?

(assume all coefficients must be real)

• $f\left(x\right)=\left(x+1\right)\left(x+4\right)\left(x+4\right)$

• $f\left(x\right)=\left(x+1\right)\left(x+1\right)\left(x+4\right)$

• $f\left(x\right)=\left(x-1\right)\left(x-4\right)\left(x-4\right)$

• $f\left(x\right)=\left(x-1\right)\left(x-1\right)\left(x-4\right)$

Tags

CCSS.HSA.APR.B.3

The polynomial function h(x) at the right has one of its zeros at x = i.

Which of the below could be a correct polynomial function for the graph shown at the right based on it zeros?

(assume all coefficients must be real)

• $h\left(x\right)=\left(x-i\right)\left(x+3\right)$

• $h\left(x\right)=\left(x-i\right)\left(x+i\right)\left(x+3\right)$

• $h\left(x\right)=\left(x+i\right)\left(x-3\right)$

• $h\left(x\right)=\left(x-i\right)\left(x+i\right)\left(x-3\right)$

Tags

CCSS.HSA.APR.B.3

Which polynomial function graphed below that has a real zero of multiplicity 2?

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Factor.

 $a^2b^6-x^8y^2$  

•  $\left(a^2+b^6\right)\left(x^8-y^2\right)$  

•  $\left(ab^3+x^4y\right)\left(ab^3-x^4y\right)$  

•  $\left(a^4b^3+xy\right)\left(a^4b^3-xy\right)$  

•  $\left(ab^3\right)\left(b^4+x^4y\right)$  

Tags

CCSS.HSA.APR.C.4

Which of the below is a factor of  

 $x^6+27$  

•  $\left(x^3+3\right)$  

•  $\left(x^2+3\right)$  

•  $\left(x^2+3x+9\right)$  

•  $\left(x^4+3x^2+9\right)$  

Tags

CCSS.HSA.APR.B.2

Are each of his steps valid? If not, in which step is there an error?

• All of Vincent's steps are valid

• Vincent didn't correctly expand the binomial in Step 1.

• Vincent can't just add to the expression in Step 2.

• Vincent factored incorrectly the terms in Step 4.

Tags

CCSS.HSA.APR.C.4