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Chapter 0 – Section 05
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...  (a) If P(x) is a polynomial of degree n then P(x) will have exactly n zeroes (real or complex), some of which may repeat.  (b) Every polynomial function of degree n > 1 has exactly n complex zeroes, counting multiplicities  (c) If P(x) has a nonreal root, a+bi, where b ≠ 0, then its conjugate, a ...
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... Solving Two-Step Equations To find the solution to an equation we must isolate the variable. In other words, get the variable on one side of the equation by itself. We isolate the variable by performing operations that will eliminate (cancel) the other numbers from the expression. ...
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... Show that the every positive even integer is of the form2q and every positive odd integer is of the form2q+1where q is some integer. Use Euclid’s division algorithm to find the HCF of a)1288 and 575 b)867 and 255 Prove that is not a rational number. Find the largest positive integer that will divide ...
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System of polynomial equations

A system of polynomial equations is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k.Usually, the field k is either the field of rational numbers or a finite field, although most of the theory applies to any field.A solution is a set of the values for the xi which make all of the equations true and which belong to some algebraically closed field extension K of k. When k is the field of rational numbers, K is the field of complex numbers.
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