Question

The hcf of two polynomials is (x + 3) and their lcm is x3 – 7x + 6. if one of the polynomials is (x2 + 2x – 3), then the other is

Answer 1

$\huge\mathbf{Solution}$
$<b>$
Let P(x) =   x² 2x – 3 =  x² + 3x – x – 3 = x(x + 3) – 1(x + 3) 

= (x + 3)(x – 1) 

LCM = x^3 – 7x + 6 =  x²(x – 1) + x(x – 1) – 6(x – 1) = (x – 1)( x² + x – 6) 

Let other polynomial be Q(x), 

P(x)×Q(x) = (HCF)×(LCM) 

Hence, Q(x) = [(HCF)×(LCM)]/[P(x)] 

= [(x + 3)×(x – 1)×( x² + x – 6)]/[±(x + 3)×(x – 1)] 

= ( x²+ x – 6) [Ans.] 

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