Question

If HCF and LCM of two polynomials P(x) and Q(x) are x(x+p) and 12x^2(x-p)(x^2-p^2) respectively. If P(x) = 4x^2(x+p), then Q(x) =​

Answer 1

Answer:

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Answer 2

Answer: Q(x)=3x(x-p)(x^2-p^2)

Step-by-step explanation:

The largest term that divides evenly into all the terms from a group is known as the highest common factor (H.C.F.).

The smallest word that is a multiple of all the numbers in a group is called the Lowest Common Multiple (L.C.M.).

HCF and LCM of Two Polynomials Relationship

The relationship between a polynomial's L.C.M. and H.C.F. is that a polynomial's product is equal to the sum of its H.C.F. and L.C.M. The following statement describes this relationship.

LCM of p(x) and q(x) * HCF of p(x) and q(x) = p(x) * q(x)

We know, $P(x)\times Q(x)=HCF\times LCM$

$x(x+p) \times 12x^2(x-p)(x^2-p^2)= 4x^2(x+p)\times Q(x)\\Q(x)=\frac{ x(x+p) \times 12x^2(x-p)(x^2-p^2)}{4x^2(x+p)}\\Q(x)=3x(x-p)(x^2-p^2)$

To know more about HCF and LCM, click on the links below:

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