16. If (x+a) is the factor of the polynomial x4px+q and x-mxin, prove that a

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( x^{2}+p x+q quad 4 quad x^{2}+m x+n ) (c) a) is factor for both polynomials ( therefore e_{cdot}, x^{2}+p x+q=(x+a)(x+underline{theta})_{4} ) ( x^{2}+m x+n=(x+a)(x+beta) ) If ( f^{2}+P x+q=(x+a)(x+alpha)=0 ) [ begin{array}{l} text { If } x=-a begin{aligned} (a)^{2}-p a+q &=0 a^{2}-p a+q &=0 rightarrow 0 end{aligned} end{array} ] If ( x^{2}+m x+n=(x+a)(x+beta)=0 ) If ( x=-a ) [ begin{array}{c} a^{2}-m a+n=0 rightarrow(2) e q 0-e x(2) a^{2}-p a+q-a^{2}+m a-n=0 a(m-p)=n-2 quad a=frac{n-q}{m-p} end{array} ]

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