Find the other polynomial q(x) of each of the following, given that LCM and GCD and one polynomial p(x) respectively.
(x3 – 4x) (5x + 1), (5 x2 + x), (5 x3 – 9 x2 – 2x).
Given: –
Polynomials p(x) = (5x3 – 9x2 – 2x)
And GCD[Greatest Common Divisor] = (5x2 + x)
And LCM[Lowest Common Multiple] = (x3 – 4x)(5x + 1)
Formula used: –
The product of 2 polynomial is equal to product of their LCM
and GCD.
Product of 2 polynomial = LCM × GCD
p(x) × q(x) = LCM × GCD
LCM × GCD = (x3 – 4x) (5x + 1) × (5x2 + x)
= x(x2 – 4)(5x + 1) × x(5x + 1)
= x2(x + 2)(x – 2)(5x + 1)(5x + 1)
p(x) = (5 x3 – 9 x2 – 2x)
= x(5x2 – 9x – 2)
= x(5x2 – 10x + x – 2)
= x[5x(x – 2) + 1(x – 2)]
= x(5x + 1)(x – 2)
p(x) × q(x) = LCM × GCD
q(x) = 
q(x) = 
q(x) = 
q(x) = x(x + 2)(5x + 1)
Conclusion: –
The other polynomial term q(x) is x(x + 2)(5x + 1)
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.