Multiply these polynomials. (x+1)(x^4+8x^2+3x+1)
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x^5+x^4+8x^3+11x^2+4x+1
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Multiply all the terms in the second set of parentheses by all of them in the first and then combine like terms
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x^5+8x^3+3x^2+x+ x^4+8x^2+3x+1
= x^5+x^4+8x^3+11x^2+4x+1
= x^5+x^4+8x^3+11x^2+4x+1