Question

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if HCF and LCM of p(x) and q(x) are 2x-1 and 6x^3+25x^2-24x+5 respectively if p(x)=2x^2+9x-5 then find the value of q(x)​

Answer 1

Answer:

• The answer is:  [q(x) = 6x^2-5x+1].

Step-by-step explanation:

• For any 2 positive integers a and b:-

HCF (a,b) * LCM (a,b) = a*b

• Thus, HCF [ p(x) and p(q) ] * LCM [ p(x) and p(q) ] = p(x) * p(q)

---  (2x-1) [ 6x^3+25x^2-24x+5 ] = [ 2x^2+9x-5 ] q(x)

--- 12x^4 + 50x^3 - 48x^2 + 10x - 6x^3 - 25x^2 + 24x-5 = q(x) [ 2x^2+9x-5 ]

--- 12x^4 + 44x^3 - 73x^2 + 34x - 5 = q(x) [2x^2+9x-5]

--- q(x) = 12x^4 + 44x^3 - 73x^2 + 34x - 5

                      2x^2+9x-5

• Now perform the long division method to get the quotient: 6x^2- 5x +1

Thus, q(x) = 6x^2 - 5x + 1.

Now you can verify by multiplying q(x) and p(x) to get HCF * LCM

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