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Examples

July 22, 2020
Category: Examples

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(1) What should be added to 3x² – 5x + 9 to get x² – 2x – 3 ?

Soln. Let, 3x² – 5x + 9 + p(x) = x² – 2x – 3

$\therefore$ p(x) = x² – 2x – 3 – 3x² + 5x – 9

= – 2x² + 3x – 12

(2) What must be subtracted from 3x² – 5x + 9 to get x² – 2x – 3 ?

Soln. Let, 3x² – 5x + 9 – p(x) = x² – 2x – 3

$\therefore$ 3x² – 5x + 9 – x² + 2x + 3 = p(x)

$\therefore$ p(x) = 2x² – 3x + 12

(3) What must be subtracted from $\frac{9x}{x^{2}+x-20}$ to get $\frac{5}{x+5}$ ?

Soln. $\frac{9x}{x^{2}+x-20}$ – p(x) = $\frac{5}{x+5}$

$\therefore \frac{9x}{(x+5)(x-4)}$ – $\frac{5}{x+5}$ = p(x)

p(x) = $\frac{4}{x+4}$

(4) Find the product : ( x² – 3x – 4 ) $\times \frac{1}{\left (x^{2}-2x-8 \right )}$

Soln. ( x² – 3x – 4 ) $\times \frac{1}{\left (x^{2}-2x-8 \right )}$

= ( x – 4 ) ( x + 1 ) $\times \frac{1}{(x-4)(x+2)}$

= $\frac{x+1}{x+2}$

(5) Simplify : $\left \{ \frac{\left (x^{2}-5x+6 \right )}{\left (x^{2}-4 \right )} \times \frac{\left (x^{2}+x-2 \right )}{\left (x^{2}-2x+3 \right )} \right \}$

Soln. $\left \{ \frac{\left (x^{2}-5x+6 \right )}{\left (x^{2}-4 \right )} \times \frac{\left (x^{2}+x-2 \right )}{\left (x^{2}-2x+3 \right )} \right \}$

= $\frac{(x-2)(x-3)}{(x+2)(x-2)} \times \frac{(x+2)(x-1)}{(x-3)(x+1)}$

= $\frac{x-1}{x+1}$

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