Question

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4. The LCM and HCF of two polynomials p(x) and q(x)
36x3(x + a) (x3 - a 3) and
x²(x - a),
respectively. If p(x) = 4x (x 2 - a2), then the value
of q(x) is
​

Answer 1

Answer:

q(x)= 27x(x³-a³)

Step-by-step explanation:

If a and b are two numbers ,then

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

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

Here,

p(x) * q(x) = LCM {p(x),q(x)} * {HCF p(x),q(x)}

So,

q(x) = LCM {p(x),q(x)} * {HCF p(x),q(x)} / p(x)

= {36*3(x+a)(x³-a³) × x²(x-a)} / 4x(x²-a²)

= 108(x³-a³)* x²* (x+a)(x-a) / 4x (x²-a²)

= 108(x³-a³)* x²* (x²-a²) / 4x (x²-a²)

= 27x(x³-a³)- ANSWER

Answer 2

Final answer:   $q(x) =(9x^{4}(x^{3} - a^{3}))$

Given that: We are given H.C.F and L.C.M of  p(x) and q(x) are $x^{2} (x - a)$ and $36x^{3} (x + a) (x^{3} - a^{3})$. $p(x) = 4x (x^{2} - a^{2} )$.

To find: We have to find the value of q(x).

Explanation:

• Given that:

H.C.F of  p(x) and q(x) =  $x^{2} (x - a)$

L.C.M of p(x) and q(x) = $36x^{3} (x + a) (x^{3} - a^{3})$

$p(x) = 4x (x^{2} - a^{2} )$

• q(x)=?. We have to find the q(x).

• The product of two polynomial = The product of their L.C.M and H.C.F

• Using this  formula,

$p(x)*q(x) = H.C.F * L.C.M$

$q(x)=\frac{(H.C.F *L.C.M)}{p(x)}$

$q(x)= \frac{(x^{2} (x - a)36x^{3} (x + a) (x^{3} - a^{3}))}{(4x (x^{2} - a^{2}))}$

$q(x)= \frac{(x(x - a)9x^{3} (x + a) (x^{3} - a^{3}))}{(x^{2} - a^{2})}$

$q(x)= \frac{(9x^{4}(x - a)(x + a) (x^{3} - a^{3}))}{(x^{2} - a^{2})}$

• we know that, $(x-a)(x+a)=x^{2} -a^{2}$

Substitute $x^{2} -a^{2}$ for $(x-a)(x+a)$ in the numerator.

$q(x)= \frac{(9x^{4}(x^{2} - a^{2} ) (x^{3} - a^{3}))}{(x^{2} - a^{2})} \\\\q(x) =(9x^{4}(x^{3} - a^{3}))$

• Therefore, the other polynomial $q(x) =(9x^{4}(x^{3} - a^{3}))$

To know more about the concept please go through the links

https://brainly.in/question/1086386

https://brainly.in/question/23071329

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