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Factorisation by Common Factors

Find the HCF ...

Question

Find the HCF of $x^{2} - 5 x + 6 a n d x^{2} - 9$

x - 3

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x + 3

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x - 4

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x + 4

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Solution

The correct option is A $x - 3$
$x^{2} - 5 x + 6 = x^{2} - 2 x - 3 x + 6$
$= x (x - 2) - 3 (x - 2)$
$= (x - 2) (x - 3)$

$x^{2} - 9$ $= (x - 3) (x + 3)$

$∴ H C F o f (x^{2} - 5 x + 6) a n d (x^{2} - 9) = x - 3$

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Similar questions

x^{4} - 11 x^{2} + 10, x^{2} - 5 x + 4 a n d x^{3} - 3 x^{2} + 3 x - 1

\frac{x - 3}{x - 4}

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

x^{2} - x - 6 a n d x^{2} + 9 x + 14

Find and correct the errors in the following mathematical statement. Substituting x = −3 in

(a) x² + 5x + 4 gives (−3)² + 5 (−3) + 4 = 9 + 2 + 4 = 15

(b) x² − 5x + 4 gives (−3)² − 5 (−3) + 4 = 9 − 15 + 4 = −2

x = - 3

x^{2} + 5 x + 4

(- 3)^{2} + 5 (- 3) + 4 = 9 + 2 + 4 = 15

x^{2} - 5 x + 4

(- 3)^{2} - 5 (- 3) + 4 = 9 - 15 + 4 = - 2

x^{2} + 5 x

(- 3)^{2} + 5 (- 3) = - 9 - 15 = - 24

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