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Addition and Subtraction of Algebraic Expression

Add: 2x3 m...

Question

Add:
2x³ − 9x² + 8, 3x² − 6x − 5, 7x³ − 10x + 1 and 3 + 2x − 5x² − 4x³

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Solution

On arranging the terms of the given expressions in the descending powers of $x$ and adding column-wise:

$2 x^{3} - 9 x^{2} + 0 x + 8 0 x^{3} + 3 x^{2} - 6 x - 5 7 x^{3} + 0 x^{2} - 10 x + 1 - 4 x^{3} - 5 x^{2} + 2 x + 3 5 x^{3} - 11 x^{2} - 14 x + 7$

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Q. Add the following:

2 x^{3} - 9 x^{2} + 8, 3 x^{2} - 6 x - 5, 7 x^{3} - 10 x + 1

3 + 2 x - 5 x^{2} - 4 x^{3}

2 x^{3} - 9 x^{2} + 10 x

(2 x + 5)

and also verify the result.

Q. Find the intervals in which the following functions are increasing or decreasing.
(i) f(x) = 10 − 6x − 2x²

(ii) f(x) = x² + 2x − 5

(iii) f(x) = 6 − 9x − x²

(iv) f(x) = 2x³ − 12x² + 18x + 15

(v) f(x) = 5 + 36x + 3x² − 2x³

(vi) f(x) = 8 + 36x + 3x² − 2x³

(vii) f(x) = 5x³ − 15x² − 120x + 3

(viii) f(x) = x³ − 6x² − 36x + 2

(ix) f(x) = 2x³ − 15x² + 36x + 1

(x) f(x) = 2x³ + 9x² + 12x + 20

(xi) f(x) = 2x³ − 9x² + 12x − 5

(xii) f(x) = 6 + 12x + 3x² − 2x³

(xiii) f(x) = 2x³ − 24x + 107

(xiv) f(x) = −2x³ − 9x² − 12x + 1

(xv) f(x) = (x − 1) (x − 2)²

(xvi) f(x) = x³ − 12x² + 36x + 17

(xvii) f(x) = 2x³ − 24x + 7

(xviii)

f (x) = \frac{3}{10} x^{4} - \frac{4}{5} x^{3} - 3 x^{2} + \frac{36}{5} x + 11

(xix) f(x) = x⁴ − 4x

(xx)

f (x) = \frac{x^{4}}{4} + \frac{2}{3} x^{3} - \frac{5}{2} x^{2} - 6 x + 7

(xxi) f(x) = x⁴ − 4x³ + 4x² + 15

(xxii) f(x) = 5x³^/2 − 3x⁵^/2, x > 0

(xxiii) f(x) = x⁸ + 6x²

(xxiv) f(x) = x³ − 6x² + 9x + 15

(xxv)

f (x) = {\{x (x - 2)\}}^{2}

Q. The number of solution of

\sqrt{3 x^{2} + 6 x + 7} + \sqrt{5 x^{2} + 10 x + 14} = 4 - 2 x - x^{2}

\frac{6 x^{2} + 13 x - 5}{9 x^{2} + 3 x - 2} \times \frac{3 x^{2} - 10 x - 8}{16 x^{2} - 1} .

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