Free Printable Roots of Polynomials Test Review

1.

Factor the polynomial and state the roots. $x^3+2x^2+4x+8=0$

a)

$\left\{2,\ 2i,\ -2i\right\}$

b)

$\left\{-2,\ 2i,\ -2i\right\}$

c)

$\left\{-2,\ 2,\ -2i,\ 2i\right\}$

d)

$\left\{2,\ 2i\right\}$

2.

Factor each polynomial and state the roots. $x^4-12x^2+32=0$

a)

$\left\{2,\ \ 2\sqrt{2}\right\}$

b)

$\left\{2,\ -2,\ 2\sqrt{2}\right\}$

c)

$\left\{2,\ -2,\ \sqrt{8}\right\}$

d)

$\left\{2,-2,\ 2\sqrt{2},-2\sqrt{2}\right\}$

3.

Write a polynomial function of least degree in standard form that has the follow roots.
$-3,\ \sqrt{5}$

a)

$f\left(x\right)=\left(x+3\right)\left(x^2-5\right)$

b)

$f\left(x\right)=\left(x-3\right)\left(x-\sqrt{5}\right)$

c)

$f\left(x\right)=x^3+3x^2-5x-15$

d)

$f\left(x\right)=x^3-3x^2+5x+15$

4.

Write a polynomial function of least degree in standard form that has the follow roots.
$3,\ -3i$

a)

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

b)

$f\left(x\right)=x^3-3x^2+9x-27$

c)

$f\left(x\right)=x^3+3x^2+9x-27$

d)

$f\left(x\right)=\left(x-3\right)\left(x-3i\right)$

5.

Use the graphing calculator to find the number and type of roots of the polynomial function. $f\left(x\right)=x^5+5x^4-x^3-5x^2-20x-100$

a)

5 total roots
1 real rational root at -5
2 real irrational roots at $\pm2.236$
2 non-real complex roots

b)

5 total roots
1 real rational root at -5
1 real irrational root at $2.236$
2 non-real complex roots

c)

5 total roots
3 real rational roots at -5, -2.236, 2.236

0 real irrational roots

2 non-real complex roots

d)

4 total roots
1 real rational root at -5
2 real irrational roots at $\pm2.236$
2 non-real complex roots

6.

Use the graphing calculator to find the number and type of roots of the polynomial function.
$f\left(x\right)=x^4-5x^2-14$

a)

4 total roots
2 real rational roots at $\left\{-7,\ 7\right\}$
2 non-real complex roots

b)

4 total roots

1 real rational root at $\left\{-7\right\}$
1 real irrational root at $\left\{\sqrt{7}\right\}$
2 non-real complex roots

c)

4 total roots
2 real irrational roots at $\pm\sqrt{7}$
2 non-real complex roots

d)

4 total roots

2 real rational roots at $\left\{\pm17\right\}$
2 real irrational roots at $\left\{\pm\sqrt{7}\right\}$

7.

Find all exact roots.
$f\left(x\right)=x^3-4x^2+5x-2$

a)

$\left\{2,\ 1\right\}$

b)

$\left\{-2,\ 2,\ -1,\ 1\right\}$

c)

$\left\{2,\ 1\ mult.\ 2\right\}$

d)

$\left\{2,\ 1,\ 1\right\}$

8.

Find all exact roots. $f\left(x\right)=x^3+7x^2-7x-57$

a)

$\left\{-3,\ -2\ \pm\ \sqrt{23}\right\}$

b)

$\left\{-3,\ -2,\ \pm\sqrt{23}\right\}$

c)

$\left\{3,\ -3,\ 2,\ -2,\ \pm\sqrt{23}\right\}$

d)

$\left\{-3,\ \pm\sqrt{23}\right\}$

9.

Find all exact roots. $x^5-81x=0$

a)

$\left\{0,\ 3,\ 3i\right\}$

b)

$\left\{0,\ 3,\ \pm3i\right\}$

c)

$\left\{\pm3,\ \pm3i\right\}$

d)

$\left\{0,\ \pm3,\ \pm3i\right\}$

10.

Find all exact roots. $3x^3+18x^2+22x+35=0$

a)

$\left\{5,\ -3,\ \pm\frac{5i\sqrt{3}}{6}\right\}$

b)

$\left\{-5,\ \frac{-3\pm5i\sqrt{3}}{6}\right\}$

c)

$\left\{-5,\ \frac{-3+5i\sqrt{3}}{6}\right\}$

d)

$\left\{5,\ \frac{-3\pm5i\sqrt{3}}{6}\right\}$

Roots of Polynomials Test Review

Total questions: 10

Worksheet time: 2hrs 16mins

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