Determine whether or not the polynomial p = 7X³ +25X² + 38X-5 is in the span of the following three polynomials P1 = 3X³ + 10X² +7X P2 = X³ + 3X²-2X+1 P3 = X³ + 1 in P3(R). If so, write p as a linear combination of P1, P2 and P3. Justify your answer.

Q: Why is a polynomial be thought as adding terms, even if some coefficients are negative

A: Why is a polynomial be thought as adding terms, even if some coefficients are negative

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Q: Express as a polynomial.

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A: We use long division method for solving these problems

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A: Solution is given below:

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Q: write a polynomial in standard form that has the given zeros: 1,-2+√7, -2-√7

A: Given problem:- write a polynomial in standard form that has the given zeros: 1,-2+√7, -2-√7