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Let f(x) = 2x2 – 7x + 5 and g(x) = x2 + 9. Find f +9, f-9, f.g, and Simplify your answers.g6121. f+g=2. f-9=3. f.g=f4.9tes0/14)Answers (in progress)

Let f(x) = 2x2 – 7x + 5 and g(x) = x2 + 9. Find f +9, f-9, f.g, and Simplify your-example-1
User Dened
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Answer

1. f + g = 3x² - 7x + 14

2. f - g = x² - 7x - 4

3. f.g = (x - 1)(2x -5)(x² + 9)

4. f/g = 2 -7x -13/x² + 9

Step-by-step explanation

Given functions:

f(x) = 2x² - 7x + 5

g(x) = x² + 9

1. f + g = (2x² - 7x + 5) + (x² + 9)

= 2x² - 7x + 5 + x² + 9

= 2x² + x² - 7x + 5 + 9

= 3x² - 7x + 14

2. f - g = (2x² - 7x + 5) - (x² + 9)

= 2x² - 7x + 5 - x² - 9

= 2x² - x² - 7x + 5 - 9

= x² - 7x - 4

3. f.g

= (2x² - 7x + 5)(x² + 9)

= 2x²(x² + 9) - 7x(x² + 9) + 5(x² + 9)

= 2x⁴ + 18x²- 7x³ - 63x + 5x² + 45

= 2x⁴ - 7x³ + 18x² + 5x² - 63x + 45

= 2x⁴ - 7x³ + 23x² - 63x + 45

Using the rational root theorem

= (x - 1) 2x⁴ - 7x³ + 23x² - 63x + 45/x - 1

= 2x⁴ - 7x³ + 23x² - 63x + 45/x-1

= 2x³ - 5x² + 18x - 45

= (x -1)(2x³ - 5x² + 18x - 45)

Now, fatorising 2x³ - 5x² + 18x - 45 yields

= (2x -5)(x² + 9)

Hence, 2x⁴ - 7x³ + 23x² - 63x + 45 = (x - 1)(2x -5)(x² + 9)

Let f(x) = 2x2 – 7x + 5 and g(x) = x2 + 9. Find f +9, f-9, f.g, and Simplify your-example-1
User Michele Volpato
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