Question

Assertion (A): p(x) = 14x³ - 2x² + 8x* +7x-8 is a polynomial of degree 3. Reason (R): The highest power of x in the polynomial p(x) is the degree of the polynomial.​

Answer 1

SOLUTION

TO DETERMINE

Assertion (A) : p(x) = 14x³ - 2x² + 8x⁴ + 7x - 8 is a polynomial of degree 3.

Reason (R): The highest power of x in the polynomial p(x) is the degree of the polynomial.

CONCEPT TO BE IMPLEMENTED

POLYNOMIAL

Polynomial is a mathematical expression consisting of variables, constants that can be combined using mathematical operations addition, subtraction, multiplication and whole number exponentiation of variables

DEGREE OF A POLYNOMIAL

Degree of a polynomial is defined as the highest power of its variable that appears with nonzero coefficient

When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term.

EVALUATION

Here the given polynomial is

p(x) = 14x³ - 2x² + 8x⁴ + 7x - 8

Which can be rewritten as

p(x) = 8x⁴ + 14x³ - 2x² + 7x - 8

The variable is x

Now the highest power of its variable that appears with nonzero coefficient

So degree of the polynomial = 4

So the Assertion is wrong

In reason it is given that the highest power of x in the polynomial p(x) is the degree of the polynomial.

So the reason is right

FINAL ANSWER

Hence the Assertion is wrong but Reason is right

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Answer 2

Step-by-step explanation:

SOLUTION

TO DETERMINE

Assertion (A) : p(x) = 14x³ - 2x² + 8x⁴ + 7x - 8 is a polynomial of degree 3.

Reason (R): The highest power of x in the polynomial p(x) is the degree of the polynomial.

CONCEPT TO BE IMPLEMENTED

POLYNOMIAL

Polynomial is a mathematical expression consisting of variables, constants that can be combined using mathematical operations addition, subtraction, multiplication and whole number exponentiation of variables

DEGREE OF A POLYNOMIAL

Degree of a polynomial is defined as the highest power of its variable that appears with nonzero coefficient

When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term.

EVALUATION

Here the given polynomial is

p(x) = 14x³ - 2x² + 8x⁴ + 7x - 8

Which can be rewritten as

p(x) = 8x⁴ + 14x³ - 2x² + 7x - 8

The variable is x

Now the highest power of its variable that appears with nonzero coefficient

So degree of the polynomial = 4

So the Assertion is wrong