Question

Q1.THE GCD OF a^3 + 2a^2 – 3a and 2a^3 + 5a^2 – 3a​.

Answer 1

Step-by-step explanation:

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

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

$\sf{= a(2{a}^{2} + 5 a - 3)} \\ </p><p></p><p>\sf{= a(2{a}^{2} + 6a - a - 3)}\\ </p><p></p><p>\sf{= a(2a - 1)(a + 3)}$

Hence the required GCD = a( a + 3 )

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Answer 2

Question :-

The GCD Of a^3 + 2a^2 – 3a and 2a^3 + 5a^2 – 3a.

Answer step by step :-

LCM = (X, Y) = HCF = (X, Y)X × Y

•°• LCM =( a²+5a+7)

(a⁴+3a³+5a²+26a+56)(a⁴+2a³- 4a² - a +28)

LCM = (a²+5a+7)(a²+5a+7)(a²- 2a+8)

=(a⁴+2a³+4a²-a+28) = ( a²-2a+8)

=(a⁴+2a³-4a²-a+28)