(3x^2-1)(x^3-2)+r=(3x^5+3x^3+2x^2+x+2) find r

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29-10-2016
Mathematics

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(3x^2-1)(x^3-2)+r=(3x^5+3x^3+2x^2+x+2) find r

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the domain for f(x) and g(x) is the set of all real numbers. let f(x) = 3x + 5 and g(x) = x^2. find (f - g)(x).

Panoyin Panoyin · Answer 1 · 2016-10-29T21:01:03+02:00

(x³ - 2)(3x² - 1) + r = 3x⁵ + 3x³ + 2x² + x + 2
x³(3x² - 1) - 2(3x² - 1) + r = 3x⁵ + 3x³ + 2x² + x + 2
x³(3x²) - x³(1) - 2(3x²) + 2(1) + r = 3x⁵ + 3x³ + 2x² + x + 2
3x⁵ - x³ - 6x² + 2 + r = 3x⁵ + 3x³ + 2x² + x + 2
-x³ - 6x² + 2 + r = 3x³ + 2x² + x + 2
-6x² + 2 + r = 4x³ + 2x² + x + 2
2 + r = 4x³ + 8x² + x + 2
r = 4x³ + 8x² + x