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Addition and Subtraction of Algebraic Expression

What must be ...

Question

What must be subtracted from
$x^{3} - 3 x^{2} + 5 x - 1$ to get $2 x^{3} + x^{2} - 4 x + 2$ ?

A

- x^{3} + 4 x^{2} - 9 x + 3

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B

x^{3} + 4 x^{2} - 9 x + 3

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C

x^{3} - 4 x^{2} + 9 x - 3

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D

- x^{3} - 4 x^{2} + 9 x - 3

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Solution

The correct option is D $- x^{3} - 4 x^{2} + 9 x - 3$
Let the polynomial to be subtracted be $p (x)$ .
$∴ x^{3} - 3 x^{2} + 5 x - 1 - p (x) = 2 x^{3} + x^{2} - 4 x + 2$
$x^{3} - 2 x^{3} - 3 x^{2} - x^{2} + 5 x + 4 x - 1 - 2 = p (x)$
$∴ p (x) = - x^{3} - 4 x^{2} + 9 x - 3$

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Similar questions

What must be subtracted from $(x^{3} - 3 x^{2} + 5 x - 1)$ to get $(2 x^{3} + x^{2} - 4 x + 2)$ ?

Q. What must be subtracted from

(x^{3} - 3 x^{2} + 5 x - 1)

(2 x^{3} + x^{2} - 4 x + 2)

Multiply the terms $- 3 x^{2} y^{2}, - 2 x y, 2 x^{2} y$ and verify the product for $x = 1$ and $y = 2$

\int \frac{x^{3} + 4 x^{2} + 9 x}{x^{2} + 4 x + 9} d x

Q. Find the limits :

i .

lim x \to 1 [\frac{x^{2} + 1}{x + 100}]

i i .

lim x \to 2 [\frac{x^{3} - 4 x^{2} + 4 x}{x^{2} - 4}]

i i i .

lim x \to 2 [\frac{x^{2} - 4}{x^{3} - 4 x^{2} + 4 x}]

i v .

lim x \to 2 [\frac{x^{3} - 2 x^{2}}{x^{2} - 5 x + 6}]

v .

lim x \to 1 [\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}]

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