Question

The polynomial p(x)= x^3-5x^2- x+5 is such that p(1)= 0 and p(-1)= 0. Which of these is equivalent to p(x)?​

Answer 1

Only p(1)= 0 is equivalent to p(x).

• Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. The word "polynomial" is derived from the Greek words "poly" and "nominal," which combined translate to "many phrases." A polynomial can have any number of terms but not infinite.
• Polynomial is made up of two terms, namely Poly (meaning "many") and Nominal (meaning "terms."). An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.

Here, the polynomial is given as,

$p(x)=x^{3}-5x^{2} -x+5$.

Then, putting x = 1, we get,

$p(1)=1^{3}-5 -1+5=0$.

Hence, only p(1)= 0 is equivalent to p(x).

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