Lesson 2 Pascal’s Pride Solidify Understanding

Ready

1.

Given: $f (x) = (x + 7) (2 x - 3)$ and $g (x) = (x + 7)$ .

Find $g (x) f (x)$ .

2.

Given: $f (x) = (5 x + 7) (- 3 x + 11)$ and $g (x) = (- 3 x + 11)$ .

Find $g (x) f (x)$ .

3.

Given: $f (x) = (x + 2) (x^{2} + 3 x + 2)$ and $g (x) = (x + 2)$ .

Find $g (x) f (x)$ .

4.

Given: $f (x) = (5 x - 3) (x^{2} - 11 x - 9)$ and $g (x) = (5 x - 3)$ and $h (x) = (x^{2} - 11 x - 9)$ .

a.

Find $g (x) f (x)$ .

b.

Find $h (x) f (x)$ .

5.

Given: $f (x) = (5 x - 6) (2 x^{2} - 5 x + 3)$ and $g (x) = (x - 1)$ and $h (x) = (2 x - 3)$ .

a.

Find $g (x) f (x)$ .

b.

Find $h (x) f (x)$ .

Set

Multiply. Write your answers in standard form.

6.

$(a + b) (a + b)$

7.

$(x - 3) (x + 9)$

8.

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

9.

$(3 x + 1) (x + 1)$

10.

$(6 x + 7) (5 x - 4)$

11.

$(2 x - 7) (x^{2} + 2)$

Write each polynomial is standard form. Pascal’s Triangle can be used as a tool, if desired.

${(x + a)}^{0}$	$1$	$1$
${(x + a)}^{1}$	$x + a$	$1 1$
${(x + a)}^{2}$	$x^{2} + 2 a x + a^{2}$	$1 2 1$
${(x + a)}^{3}$	$x^{3} + 3 a x^{2} + 3 a^{2} x + a^{3}$	$1 3 3 1$
${(x + a)}^{4}$	$x^{4} + 4 a x^{3} + 6 a^{2} x^{2} + 4 a^{3} x + a^{4}$	$1 4 6 4 1$

12.

$p (x) = {(x + 1)}^{5}$

13.

$p (x) = {(x - y)}^{3}$

14.

$p (x) = {(x - 1)}^{4}$

15.

$p (x) = {(x + 4)}^{3}$

16.

$p (x) = {(x + 2)}^{4}$

17.

$p (x) = {(3 x + 1)}^{3}$

Go

Graph each function.

18.

$h (x) = x^{2} + 2$

19.

$f (x) = 2^{x} + 2$

20.

$h (x) = 3 {(x - 2)}^{2}$

21.

$f (x) = | x - 1 | - 2$

22.

$h (x) = \frac{1}{2} {(x - 1)}^{2} - 2$