Question: Hello guys. i need help for this question Given the following set S of polynomials , find a polynomial p ( x )in 4 so

Hello guys. i need help for this question

Given the following setSof polynomials , find a polynomialp(x)in4so thatS{p(x)}spans4and a non-zero polynomialq(x)in4so thatS{q(x)}does not span4.

Use the '^' character to indicate an exponent, e.g.5x^22x+1.

S = {10x4+9x3+5x25x1,5x4+7x3+2x28x5 , 6x4+7x310x28x+6,5x4+x3+7x24x6 }

p(x) and q(x) ?

THanks!

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