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Find all zeros and write a linear factorization of the function

Use the Intermediate Value theorem to find an approximation for this zero to the nearest tenth. Once we have done this, we can use synthetic division repeatedly to determine all of the zeros of a polynomial function.

They want the length of the cake to be four inches longer than the width of the cake and the height of the cake to be one-third of the width. Use synthetic division to evaluate a given possible zero by synthetically dividing the candidate into the polynomial.

Use synthetic division to divide the polynomial by Confirm that the remainder is 0. Since - 4 is a lower bound and 4 is an upper bound for the real roots of the equation, then that means all real roots of the equation lie between - 4 and 4.

A complex number is not necessarily imaginary. Since we are looking for a degree 4 polynomial, and now have four zeros, we have all four factors.

Use the Linear Factorization Theorem to find polynomials with given zeros. This pair of implications is the Factor Theorem. Given a factor and a third-degree polynomial, use the Factor Theorem to factor the polynomial.

When the leading coefficient is 1, the possible rational zeros are the factors of the constant term. Only multiplication with conjugate pairs will eliminate the imaginary parts and result in real coefficients.

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Zeros and multiplicity