1. factor: k^2+2k-24
2. factor: 4k^2-1
3. factor: 25b^2-30b+9
4. solve by factoring: x^2+11x+28=0
5.find the product. write your answer in standard form: (3a+8)(3a^2-a-7)

1.  k^2+2k-24

1A. (k - 4) (k + 6)

2. 4k^2-1

2A. (2k + 1) (2k - 1)

3. 25b^2-30b+9

3A. (5b - 3)^2

4. x^2+11x+28=0

4A. x = (-4) OR (-7)

5. (3a+8)(3a^2-a-7)

5A. 9a^2 + 21a^2 - 29a - 56

Step-by-step explanation:

1.  k^2+2k-24

Factor using the AC factoring method.

k^2 = 2k

2k + 2k - 24

(k - 4) (k +6)

2. 4k^2-1

Use the Difference of Squares Formula: a^2 - b^2 = (a + b)(a - b)

2k = a

1 = b

(2k + 1)(2k - 1)

3. 25b^2-30b+9

Use the perfect square rule

(5b - 3)(5b - 3)

(5b - 3)^2

4. x^2+11x+28=0

Factor, by setting each factor equal to 0

x^2+11x+28=0

(x + 4)(x + 7) = 0

x = (-4) OR (-7)

5. (3a+8)(3a^2-a-7)

Simply, multiply each term in the first expression by each term in the second expression, and then simplify.

(3a+8)(3a^2-a-7)

9a^2 + 21a^2 - 29a - 56

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

a.)the line for function b is steeper