Which of the following expressions are factorizable ?

x^{2} - 3 x - 54

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x (2 x - 1) - 1

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3 x^{2} + 4 x - 10

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2 x^{2} + 2 x - 75

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Solution

The correct options are
A $x^{2} - 3 x - 54$
B $x (2 x - 1) - 1$
$1. x^{2} - 3 x - 54$

Comparing the given expression with $a x^{2} + b c + c$ , we get

$a = 1, b = - 3, c = - 54$

$\Rightarrow b^{2} - 4 a c = (- 3)^{2} - 4 (1) (- 54)$

$= 9 + 216$

$= 225$

225 is a perfect square.
$∴ x^{2} - 3 x - 54$ is factorizable.

$2. x (2 x - 1) - 1$

$\Rightarrow 2 x^{2} - x - 1$

Comparing the given expression with $a x^{2} + b c + c$ , we get

$a = 2, b = - 1, c = - 1$

$\Rightarrow b^{2} - 4 a c = (- 1)^{2} - 4 (2) (- 1)$

$= 1 + 8$

$= 9$

9 is a perfect square.
$∴ x (2 x - 1) - 1$ is factorizable.

$3. 3 x^{2} + 4 x - 10$

Comparing the given expression with $a x^{2} + b c + c$ , we get

$a = 3, b = 4, c = - 10$

$\Rightarrow b^{2} - 4 a c = (3)^{2} - 4 (3) (- 10)$

$= 9 + 120$

$= 129$

129 is not a perfect square.
$∴ x^{2} - 3 x - 54$ is not factorizable.

$4. 2 x^{2} + 2 x - 75$

Comparing the given expression with $a x^{2} + b c + c$ , we get

$a = 2, b = 2, c = - 75$

$\Rightarrow b^{2} - 4 a c = (2)^{2} - 4 (2) (- 75)$

$= 4 + 600$
$= 604$

604 is not a perfect square.
$∴ 2 x^{2} + 2 x - 75$ is not factorizable.

Suggest Corrections

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