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2 years ago

Factor the polynomial F(x) =x^3-x^2-4x+4 completely.

Mathematics

1 answer:

Norma-Jean [14]2 years ago

6 0

Answer:

Step-by-step explanation:

PART 1:

Possible roots by noticing the coefficient of first term:

x = 1, -1

PART 2:

1 | 1 -1 -4 4

1 0 -4 0

The remainder is zero, hence one factor is (x-1)

PART 3:

$x^3-x^2-4x+4=(x^2-4)(x-1)\\\\x^3-x^2-4x+4=(x+2)(x-2)(x-1)$

PART 4:

$f(x)=(x+2)(x-2)(x-1)\\\\=(x^2-4)(x-1)\\\\=x^3-4x-x^2+4\\\\=x^3-x^2-4x+4$

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Answer:

The height of the prism is $1\frac{1}{6}$ units ⇒ answer a

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Step-by-step explanation:

* Lets explain how to solve the problem

- The volume of a rectangular prism is

→ V = Area of the base × its height

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∴ $3\frac{25}{36}=3\frac{1}{6}*h$

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* The height of the prism is $1\frac{1}{6}$ units

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- The number of blocks = volume of the prism ÷ volume of the block

∵ The volume of the prism is $3\frac{25}{36}$ units³

∵ The volume of each block is $\frac{1}{36}$ units³

∴ The number of blocks = $3\frac{25}{36}$ ÷ $\frac{1}{36}=133$

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This is a 3-4-5 triangle.

Remember,
SOH-CAH-TOA

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