Question

The value of a polynomial f(x) for x = a where a is real number or a complex number is denoted by f(a). In particular, if the coefficients a0, a1, a2, a3, .... of a polynomial f(x) be all real numbers, the polynomial f(x) is said to be a real polynomial.

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Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

A polynomial is as expression such as x5 − 2x3 + 8x + 3 or G3t1.pdfx4 − G3g1.pdfx2 + 1. There may be any number of terms, but each term must be a multiple of a whole number power of x. Thus 2x3 − x is not a polynomial.

The term with the highest power of is called the leading term and its coefficient is called the leading coefficicent. If the leading coefficient is 1, then the polynomial is called monic. The index of the leading term is called the degree of the polynomial. The term independent of is called the constant term.

Thus x5 − 2x3 + 8x + 3 is a monic polynomial of degree 5 with constant term 3, while

G3t3.pdfx4 − G3g2.pdfx2 + 1 is a non-monic polynomials of degree 4 with leading coefficient and constant term 1.

In the first polynomial, the coefficients are all integer while the second polynomials has an irrational coefficient. For the most part, we will consider only polynomials of the first type, but much of what follows applies equally well to the second.

To name polynomials, we will use the function notation such as p(x) or q(x). Thus we can write p(x) = x5 − 2x3 + 8x + 3, or q(x) = G3t5.pdfx4 − x2 + 1. This enables us to conveniently substitute values of x when required.

The general polynomial has the form

p(x) = anxn − an − 1xn − 1 + ... + a1x + a0,

where an ≠ 0 and n is a whole number. The coefficients are, in general, real numbers.