given the LCM and GCD of the two polynomials are a^3-10^2+11a+70 and and the Polynomials p(x) is a^2-12a+35then find q(x)
Answers
Answered by
0
h(a)=a−7 and LCM m(a)=a
3
−10a
2
+11a+70.
p(a)=a
2
−12a+35
=a
2
−7a−5a+35
=a(a−7)−5(a−7)
=(a−7)(a−5)
∴p(a)=(a−7)(a−5) ......... (i)
Now, m(a)=a
3
−10a
2
+11a+70
=(a−7)(a
2
−3a−10) ........ [Using synthetic division]
=(a−7)(a
2
−5a+2a−10)
=(a−7)(a−5)(a+2)
∴m(a)=(a−7)(a−5)(a+2) ........ (ii)
q(a) will have (a−7) as one of the factor, since h(a)=a−7
From (ii) and (i), q(a) will have (a+2) as one of the factor.
Also, since h(a)⋅m(a)=p(a)⋅q(a)
⟹q(a)=(a−7)(a+2)
Hence, q(a)=a
2
−5a−14
Similar questions