Lesson 5 Divide and Conquer Solidify Understanding

Ready

Solve for $x$ .

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

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

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.

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