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yulyashka [42]
3 years ago
8

HELP !!! Place the indicated product in the proper location on the grid. Write your answer in descending powers of x. (x 2 + 2x

- 1)(x 2 + 2x + 5)
Mathematics
2 answers:
Vikentia [17]3 years ago
8 0

Answer:

x^4 + 4x^3 + 8x^2 + 8x -5

Step-by-step explanation:

To make the product of two polynomials, simply apply the distributive property of multiplication, as follows:

(x^2 + 2x - 1)*(x^2 + 2x + 5)

x^2*x^2 + x^2*2x + x^2*5 + 2x*x^2 + 2x*2x + 2x*5 - 1*x^2 - 1*2x - 1*5

x^4 + 2x^3 + 5x^2 + 2x^3 + 4x^2 + 10x - x^2 - 2x - 5

x^4 + 4x^3 + 8x^2 + 8x -5

inna [77]3 years ago
6 0

Answer:

The answer to your question is:  x⁴ + 4x³ + 8x² + 8x - 5

Step-by-step explanation:

(x² + 2x - 1)(x² + 2x + 5) = x⁴ + 2x³ + 5x² + 2x³ + 4x² + 10x - x² - 2x - 5

                                       = x⁴ + 4x³ + 8x² + 8x - 5

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Step-by-step explanation:

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The 10th term in the sequence is 2560 what is the 11th term in the sequence
joja [24]

Full Question:

The 4th term of a g.p. is 40 and the 10th term in the sequence is 2560, what is the 11th term in the sequence ?

Answer:

the 11 the term is 5120

Step-by-step explanation:

Given

Geometry Progression

4th term = 40

10th term = 2560

Required

11 term.

The nth term of a geometric sequence is calculated as follows

Tₙ = arⁿ⁻¹

For the 4th term, n = 4 and Tₙ = 40

Substitute these in the given formula; this gives

40 = ar⁴⁻¹

40 = ar³. --;; equation 1

For the 10th term, n = 10 and Tₙ = 2560

Substitute these in the given formula; this gives

2560 = ar¹⁰⁻¹

2560 = ar⁹. --;; equation 2

Divide equation 2 by 1. This gives

2560/40 = ar⁹/ar³

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From laws of indices

64 = r⁹⁻³

64 = r⁶

Find 6th root of both sides

(64)^1/6 = r

r = (2⁶)^1/6

r = 2

Substitute r = 2 in equation 1

40 = ar³. Becomes

40 = a * 2³

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40 = 8a

Divide both sides by 8

40/8 = 8a/8

5 = a

a = 5.

Now, the 11 term can be solved using Tₙ = arⁿ⁻¹ where n = 11

So,

Tₙ = arⁿ⁻¹ becomes

Tₙ = 5 * 2¹¹⁻¹

Tₙ = 5 * 2¹¹⁻¹

Tₙ = 5 * 2¹⁰

Tₙ = 5 * 1024

Tₙ = 5120.

Henxe, the 11 the term is 5120

5 0
3 years ago
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