P The HCF of two polynomials \( p(x) \) and \( q(x) \) using long division method was found to b...

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The HCF of two polynomials \( p(x) \) and \( q(x) \) using long division method was found to be \( x+5 \), If their first three quotients obtained are \( x, 2 x+5 \), and \( x+3 \) respectively. Find \( p(x) \) and \( q(x) \). (The degree of \( p(x) \) the degree of \( q(x)) \)
(a) \( p(x)=2 x^{4}+21 x^{3}+72 x^{2}+88 x+15 \)
\[
q(x)=2 x^{3}+21 x^{2}+71 x+80
\]
(b) \( p(x)=2 x^{4}-21 x^{3}-72 x^{2}-88 x+15 \)
\[
q(x)=2 x^{3}+21 x^{2}-71 x+80
\]
(c) \( p(x)=2 x^{4}+21 x^{3}+88 x+15 \)
\[
q(x)=2 x^{3}+71 x+80
\]
(d) \( p(x)=2 x^{4}-21 x^{2}-72 x^{2}+80 x+15 \)
\[
q(x)=2 x^{3}-21 x^{2}+71 x+80
\]
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