Lesson 2 I Rule! Solidify Understanding

Ready

Rewrite each expression as the product of two binomials.

Each expression involves two multiplication problems separated by a $+$ or $-$ sign. Each multiplication problem contains a matching binomial factor that can be factored out so that the expression becomes a product of two binomials.

Example:

$3 x (4 x + 1) + 2 (4 x + 1) = (4 x + 1) (3 x + 2)$
Factor out $(4 x + 1)$ and write the numbers that remain $(3 x + 2)$ .
Rewrite as $(4 x + 1) (3 x + 2)$ .

1.

$2 x (5 x + 3) + 7 (5 x + 3)$

2.

$8 x (x + 1) + 2 (x + 1)$

3.

$6 x (x - 10) - 1 (x - 10)$

4.

$1 x (3 x + 4) + 5 (3 x + 4)$

5.

$3 x (8 x + 3) - 4 (8 x + 3)$

6.

$5 x (2 x + 6) + 2 (2 x + 6)$

7.

$7 x (- 5 x + 2) - 13 (- 5 x + 2)$

8.

$- 4 x (12 x + 3) + 3 (12 x + 3)$

Set

In each set of three functions, one will be linear, one will be exponential, and one will be a quadratic function. Explain the nature of change for the function and find an explicit and recursive equation for each.

9.

a.

$x$	$f (x)$
$6$	$64$
$7$	$128$
$8$	$256$
$9$	$512$
$10$	$1,024$

Type of function and nature of change:

Explicit equation:

Recursive equation:

b.

$x$	$f (x)$
$6$	$36$
$7$	$49$
$8$	$64$
$9$	$81$
$10$	$100$

Type of function and nature of change:

Explicit equation:

Recursive equation:

c.

$x$	$f (x)$
$6$	$11$
$7$	$13$
$8$	$15$
$9$	$17$
$10$	$19$

Type of function and nature of change:

Explicit equation:

Recursive equation:

10.

a.

$x$	$f (x)$
$- 2$	$- 17$
$- 1$	$- 12$
$0$	$- 7$
$1$	$- 2$
$2$	$3$

Type of function and nature of change:

Explicit equation:

Recursive equation:

b.

$x$	$f (x)$
$- 2$	$\frac{1}{25}$
$- 1$	$\frac{1}{5}$
$0$	$1$
$1$	$5$
$2$	$25$

Type of function and nature of change:

Explicit equation:

Recursive equation:

c.

$x$	$f (x)$
$- 2$	$9$
$- 1$	$6$
$0$	$5$
$1$	$6$
$2$	$9$

Type of function and nature of change:

Explicit equation:

Recursive equation:

11.

Graph the functions from the tables in problems 9 and 10. Add any additional characteristics you notice from the graph. Place the axes so that you can show all $5$ points. Identify your scale. Write the explicit equation above the graph.

a.

Equation:

b.

Equation:

c.

Equation:

d.

Equation:

e.

Equation:

f.

Equation:

Go

Find the greatest common factor (GCF) for the given values.

12.

$15$ and $25$

13.

$12$ and $32$

14.

$18$ and $54$

15.

$14$ and $21$

16.

$6$ , $18$ , and $- 12$

17.

$45$ and $36$

18.

$22$ , $33$ , and $99$

19.

$16$ , $24$ , and $36$

20.

$25$ and $36$