We can write a polynomial in a variable x of a degree n where n is any whole number.
Generally, we say
For example, the general form of a first degree polynomial in one variable x is ax+b,
where a and b are real numbers and a ¹ 0.
3.2.2 VALUE OF A POLYNOMIAL
Now consider the polynomial p(x) = x
2 – 2x – 3. What is the value of the polynomial at
any value of x? For example, what is the value at x = 1? Substituting x = 1, in the polynomial,
we get p(1) = (1)2
– 2(1) – 3 = –4. The value – 4, is obtained by replacing x by 1 in the given
polynomial p(x). This is the value of x
2 – 2x – 3 at x = 1.
Similarly, p(0) = –3 is the value of p(x) at x = 0.
Thus, if p(x) is a polynomial in x, and if k is a real number, then the value obtained by
replacing x by k in p(x), is called the value of p(x) at x = k, and is denoted by p(k).
3.2.2 VALUE OF A POLYNOMIAL
Now consider the polynomial p(x) = x
2 – 2x – 3. What is the value of the polynomial at
any value of x?