thanks in advance. i just dont understand what multiplicityis. the answer is in

Question

thanks in advance. i just dont understand what multiplicityis. the answer is in the back of my textbook and is listed, i justdo not know how to get that answer write a polynomial function in standard form with realcoefficients whose zeros and their multiplicities include thoselisted: 1 (multiplicity 2), -2 (multiplicity 3) answer:x5+4x4+x3-10x2-4x+8 thanks in advance. i just dont understand what multiplicityis. the answer is in the back of my textbook and is listed, i justdo not know how to get that answer write a polynomial function in standard form with realcoefficients whose zeros and their multiplicities include thoselisted: 1 (multiplicity 2), -2 (multiplicity 3) answer:x5+4x4+x3-10x2-4x+8

Explanation / Answer

The multiplicity of a given factor of a polynomial is the number oftimes it appears in the prime factorization. For example, ifwe look at x2-2x+1, we can see that it is equal to(x-1)2, so the factor 1 has multiplicity 2. So, tofind this, we have to take(x-1)2(x+2)3=(x2-2x+1)(x3+6x2+12x+8)=x5+6x4+12x3+8x2-2x4-12x3-24x2-16x+x3+6x2+12x+8= x5+4x4+x3-10x2-4x+8

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