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Hoochie [10]
3 years ago
8

Divide f(x) by d(x), and write a summary statement in the form indicated.

Mathematics
1 answer:
Mandarinka [93]3 years ago
3 0

Answer:

The correct option is B)  f(x) =(x^2+1)(x^2+4x+5)

Step-by-step explanation:

Consider the provided function.

f(x) = x^4 + 4x^3 + 6x^2 + 4x + 5 and d(x) = x^2+1

We need to divide f(x) by d(x)

As we know: Dividend = Divisor × Quotient + Remainder

In the above function f(x) is dividend and divisor is d(x)

Divide the leading term of the dividend by the leading term of the divisor:\frac{x^4}{x^2}=x^2

Write the calculated result in upper part of the table.

Multiply it by the divisor: x^2(x^2+1)=x^4+x^2

Now Subtract the dividend from the obtained result:

(x^4 + 4x^3 + 6x^2 + 4x + 5)-(x^4-x^2)=4x^3+5x^2+4x+5

Again divide the leading term of the obtained remainder by the leading term of the divisor: \frac{4x^3}{x^2}=4x

Write the calculated result in upper part of the table.

Multiply it by the divisor: 4x(x^2+1)=4x^3+4x

Subtract the dividend:

(4x^3+5x^2+4x+5)-(4x^3+4x)=5x^2+5

Divide the leading term of the obtained remainder by the leading term of the divisor: \frac{5x^2}{x^2}=5

Multiply it by the divisor: 5(x^2+1)=5x^2+5

Subtract the dividend:

(5x^2+5)-(5x^2+5)=0

Therefore,

Dividend = x^4 + 4x^3 + 6x^2 + 4x + 5

Divisor = x^2+1

Quotient = x^2+4x+5

Remainder = 0

Dividend = Divisor × Quotient + Remainder

f(x) = (x^2+1)(x^2+4x+5)

Hence, the correct option is B)  f(x) =(x^2+1)(x^2+4x+5)

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Answer:

A = 3 ft, B = 7 ft, C = 4 ft, D = 5 ft, Surface Area = 96 ft^2

Step-by-step explanation:

<u>Step 1:  Determine the sides</u>

A → 3 ft

B → 7 ft

C → 4 ft

D → 5 ft

<u>Step 2:  Determine the surface area</u>

Area of the sides

A= 4\ ft * 7\ ft = 28\ ft^2

A= 5\ ft * 7\ ft = 35\ ft^2

A= 3\ ft * 7\ ft = 21\ ft^2

Area of the top and bottom triangles

A= \frac{h\ *\ b}{2} = \frac{3\ ft\ *\ 4\ ft}{2} = \frac{12\ ft^2}{2} = 6\ ft^2 = 2(6\ ft^2) = 12\ ft^2

Total Area

28\ ft^2 + 35\ ft^2 + 21\ ft^2 + 12\ ft^2

96\ ft^2

Answer:  A = 3 ft, B = 7 ft, C = 4 ft, D = 5 ft, Surface Area = 96 ft^2

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