How do you factor f(x) = x^3 – 3x^2 – 10x + 24 ?

Step-by-step explanation:

I would use the Horner method.

f(x) = x³ – 3x² – 10x + 24

f(2) = 2³ - 3·2² - 10·2 +24 = 0   ⇒ x=2 is the root of function

So:

    |   1   | -3   |  -10  |  24 |

2  |   1   |  -1   |  -12  |  0   |

therefore:

f(x) = x³ – 3x² – 10x + 24 =  (x – 2)(x² – x – 12)

For  x² – x – 12:

It means:

f(x) = x³ – 3x² – 10x + 24 =  (x – 2)(x – 4)(x + 3)

Goats: 32

Cows: 24

Animals: 56

Step-by-step explanation:

Using a proportion, equivalent ratios, you can use the number of goats to find the total number of animals and then the number of cows:

, where 'x' represents the total number of animals

Cross-multiply: 4x = (32)(7) or 4x = 224

Divide: 4x/4 = 224/4 or x = 56

Total number of animals = 56

Number of goats: 32

Number of cows: 56 - 32 = 24