Lesson 6 Getting to the Root of the Problem Solidify Understanding

Ready

Order the numbers from least to greatest.

1.

$100^{3}$
$\sqrt{100}$
$\log_{2} 100$
$100$
$2^{10}$

2.

$2^{- 1}$
$- \sqrt{100}$
$\log_{2} (\frac{1}{8})$
$0$
${(- 2)}^{1}$

3.

$2^{0}$
$\sqrt{25}$
$\log_{2} 8$
$2 (x^{0}), x \neq 0$
${(2)}^{- \frac{1}{2}}$

4.

$\log_{3} 3^{3}$
$\log_{5} 5^{- 2}$
$\log_{6} 6^{0}$
$\log_{4} 4^{- 1}$
$\log_{2} 2^{4}$

Refer to the given graph to answer the questions.

Insert $>$ , $<$ , or $=$ in each statement to make it true.

5.

$f (0)$ $\underset{―}{}$ $g (0)$

6.

$f (2)$ $\underset{―}{}$ $g (2)$

7.

$f (- 1)$ $\underset{―}{}$ $g (- 1)$

8.

$f (1)$ $\underset{―}{}$ $g (- 1)$

9.

$f (5)$ $\underset{―}{}$ $g (5)$

10.

$f (- 2)$ $\underset{―}{}$ $g (- 2)$

11.

How many times does $f (x)$ equal $g (x)$ ? How do you know?

Set

Use the given root to find the remaining roots. Then write the function in factored form.

12.

Function	Roots	Factored form
$f (x) = x^{3} - 13 x^{2} + 52 x - 60$	$x = 5$ solution:	solution:

Function

Roots

Factored form

$f (x) = x^{3} - 13 x^{2} + 52 x - 60$

$x = 5$

solution:

13.

Function	Roots	Factored form
$g (x) = x^{3} + 6 x^{2} - 11 x - 66$	$x = - 6$ solution:	solution:

Function

Roots

Factored form

$g (x) = x^{3} + 6 x^{2} - 11 x - 66$

$x = - 6$

solution:

14.

Function	Roots	Factored form
$p (x) = x^{3} + 17 x^{2} + 92 x + 150$	$x = - 3$ solution:	solution:

Function

Roots

Factored form

$p (x) = x^{3} + 17 x^{2} + 92 x + 150$

$x = - 3$

solution:

15.

Function	Roots	Factored form
$q (x) = x^{4} - 6 x^{3} + 3 x^{2} + 12 x - 10$	$x = \sqrt{2}$ solution:	solution:

Function

Roots

Factored form

$q (x) = x^{4} - 6 x^{3} + 3 x^{2} + 12 x - 10$

$x = \sqrt{2}$

solution:

Go

Multiply. Combine like terms and write your answers in descending order of the exponent.

16.

$(x - \sqrt{13}) (x + \sqrt{13})$

17.

$(x - 3 \sqrt{2}) (x + 3 \sqrt{2})$

18.

$(x - 4 + 2 i) (x - 4 - 2 i)$

19.

$(x + 5 + 3 i) (x + 5 - 3 i)$

20.

$(x - 1 + i) (x - 1 - i)$

21.

$(x + 10 - i \sqrt{2}) (x + 10 + i \sqrt{2})$