Lesson 4 Divide and Conquer Solidify Understanding

Ready

Solve for $x$ . Think about the steps needed to solve different types of equations. Identify whether you isolated the variable first or if you factored first. If you did neither, explain your method.

1.

$5 x + 13 = 48$

2.

$\frac{1}{3} x - 8 = 0$

3.

$- 4 - 9 x = 0$

4.

$x^{2} - 16 = 0$

5.

$x^{2} + 4 x + 3 = 0$

6.

$x^{2} - 5 x + 6 = 0$

7.

$(x + 8) (x + 11) = 0$

8.

$(x - 5) (x - 7) = 0$

9.

$(3 x - 18) (5 x - 10) = 0$

Set

10.

a.

Divide: $(x + 1) x^{3} - 3 x^{2} + 6 x + 11$ .

b.

Write only one multiplication statement if the divisor is a factor. If there is a remainder, write the quotient in two ways.

11.

a.

Divide: $(x - 5) x^{3} - 9 x^{2} + 23 x - 15$ .

b.

Write only one multiplication statement if the divisor is a factor. If there is a remainder, write the quotient in two ways.

12.

a.

Divide: $(2 x - 1) 2 x^{3} + 15 x^{2} - 34 x + 13$ .

b.

Write only one multiplication statement if the divisor is a factor. If there is a remainder, write the quotient in two ways.

13.

a.

Divide: $(x + 4) x^{3} + 13 x^{2} + 26 x - 25$ .

b.

Write only one multiplication statement if the divisor is a factor. If there is a remainder, write the quotient in two ways.

14.

a.

Divide: $(x + 7) x^{3} - 8 x^{2} - 111 x + 10$ .

b.

Write only one multiplication statement if the divisor is a factor. If there is a remainder, write the quotient in two ways.

15.

a.

Divide: $(3 x - 4) 3 x^{3} + 23 x^{2} + 6 x - 28$ .

b.

Write only one multiplication statement if the divisor is a factor. If there is a remainder, write the quotient in two ways.

16.

Given: $f (x) = x^{3} - 3 x^{2} + 6 x + 11$

Calculate $f (- 1)$ .

17.

How does your answer to problem 16 relate to problem 10?

18.

Given: $g (x) = x^{3} + 13 x^{2} + 26 x - 25$

Calculate $g (- 4)$ .

19.

How does your answer to problem 18 relate to problem 13?

20.

Given: $h (x) = x^{3} - 8 x^{2} - 111 x + 10$

Find $h (- 7)$ .

21.

How does your answer from problem 20 relate to problem 14?

Go

Solve for $x$ . Write your answers as a logarithm and approximate the answer.

22.

$10^{4 x + 1} = 215$

23.

$\frac{10^{x}}{5} - 3 = 21$

24.

$- 16 + 10^{7 x} = 4$

25.

Given that $f (x) = \log_{3} 729 x - \log_{3} 3$ , select all of the functions equivalent to $f (x)$ .

A.

$a (x) = \log_{3} x + 5$

B.

$b (x) = \frac{\log_{3} 729 x}{\log_{3} 3}$

C.

$c (x) = \log_{3} 3 x + 2 \log_{3} 9$

D.

$d (x) = \frac{1}{2} \log_{3} 9 - \log_{3} 3 + \log_{3} 243 x$