For f (x) = x3 - 7x2 + 8x + 16, a. Find f (10) using synthetic division.

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Answer to your query is provided below

The value of f (10) using synthetic division is 396.

Explanation:

Cubic polynomials cannot be factorized by splitting the middle term. Quadratic polynomials can be factorized by splitting the middle term.

A cubic polynomial can have a maximum of three linear factors. To factorize a cubic polynomial, we first find a factor by hit and trial method or using factor theorem and reduce it into the product of a quadratic polynomial and a linear polynomial. The quadratic polynomial can then be factorized in linear factors.