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Warm-up. Factor. 1. p 2 + 6p – 27 2. p 2 – 15p – 16 3. k 2 + 9k + 204. k 2 – 14k + 24 . Warm-up. Factor. 1. p 2 + 6p – 27 2. p 2 – 15p – 16. -27. -16. -3. 9. 1. -16. 6. -15. ( p – 3)(p + 9). ( p + 1)(p – 16). Warm-up. Factor.

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Warm-up

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Warm up

Warm-up

Factor.

1. p2 + 6p – 27 2. p2 – 15p – 16

3. k2 + 9k + 204. k2 – 14k + 24


Warm up

Warm-up

Factor.

1. p2 + 6p – 27 2. p2 – 15p – 16

-27

-16

-3

9

1

-16

6

-15

(p – 3)(p + 9)

(p + 1)(p – 16)


Warm up

Warm-up

Factor.

3. k2 + 9k + 204. k2 – 14k + 24

20

24

4

5

-2

-12

9

-14

(k + 4)(k + 5)

(k – 2)(k – 12)


Warm up

Section 10.4

Solving Radical Equations (Part 2)

Standards: 2.0, 25.2

Objective: I will solve equations containing radicals.


Warm up

Extraneous Solutions:

An answer that does not solve the original equation.

x = 2

x2 = 4

(x)2 = 22

x = 2

x = -2


Warm up

Steps:

Get the radicand by itself.

Square both sides.

Solve the remaining equation.

Check your answer and identify extraneous solutions.


Warm up

Example 1:

-6

2

-3

-1

(x + 2)(x – 3) = 0

x + 6

x2 =

x + 2 = 0

x – 3 = 0

-x – 6 -x – 6

x2 – x – 6 = 0

x = -2

x = 3


Warm up

Example 1:

check x = -2 & 3

-2 = 2

3 = 3

extraneous


Warm up

Example 2:

4

-1

-4

-5

(x – 1)(x – 4) = 0

5x – 4

x2 =

x – 1 = 0

x – 4 = 0

-5x +4 -5x + 4

x2 – 5x + 4 = 0

x = 1

x = 4


Warm up

Example 2:

check x = 1 & 4

1 = 1

4 = 4


Warm up

Example 3:

-20

-4

5

1

(x – 4)(x + 5) = 0

20 – x

x2 =

x – 4 = 0

x + 5 = 0

-20 + x -20 + x

x2 + x – 20 = 0

x = 4

x = -5


Warm up

Example 3:

check x = 4 & -5

4 = 4

-5 = 5

extraneous


Warm up

Example 4:

-56

-7

8

1

(x – 7)(x + 8) = 0

56 – x

x2 =

x – 7 = 0

x + 8 = 0

-56 + x -56 + x

x2 + x – 56 = 0

x = 7

x = -8


Warm up

Example 4:

check x = 7 & -8

7 = 7

-8 = 8

extraneous


Warm up

Example 5:

-12

3

-4

-1

(x + 3)(x – 4) = 0

x + 12

x2 =

x + 3 = 0

x – 4 = 0

-x – 12 -x – 12

x2 – x – 12 = 0

x = -3

x = 4


Warm up

Example 5:

check x = -3 & 4

-3 = 3

4 = 4

extraneous


Warm up

Example 6:

-15

3

-5

-2

(x + 3)(x – 5) = 0

2x + 15

x2 =

x + 3 = 0

x – 5 = 0

-2x – 15 -2x – 15

x2 – 2x – 15 = 0

x = -3

x = 5


Warm up

Example 6:

check x = -3 & 5

-3 = 3

5 = 5

extraneous


Warm up

Example 7:

8

2

4

6

(x + 2)(x + 4) = 0

-8 – 6x

x2 =

x + 2 = 0

x + 4 = 0

8 + 6x 8 + 6x

x2 + 6x + 8 = 0

x = -2

x = -4


Warm up

Example 7:

check x = -2 & -4

-2 = 2

-4 = 4

extraneous

extraneous

no solution


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