Question

THE GCD OF a^3 + 2a^2 – 3a and 2a^3 + 5a^2 – 3a​

Answer 1

SOLUTION

TO DETERMINE

The GCD of a³ + 2a² - 3a and 2a³ + 5a² - 3a

EVALUATION

Here the given expressions are

a³ + 2a² - 3a and 2a³ + 5a² - 3a

First expression

$\sf{= {a}^{3} + 2 {a}^{2} - 3a}$

$\sf{= a( {a}^{2} + 2a - 3)}$

$\sf{= a( {a}^{2} + 3a - a - 3)}$

$\sf{= a( a - 1)(a + 3)}$

Second expression

$\sf{= 2{a}^{3} + 5 {a}^{2} - 3a}$

$\sf{= a(2{a}^{2} + 5 a - 3)}$

$\sf{= a(2{a}^{2} + 6a - a - 3)}$

$\sf{= a(2a - 1)(a + 3)}$

Hence the required GCD = a( a + 3 )

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