Question

What is the coefficient form of the polynomial
y5+3?
(A) (1, 3)
(B) (1, 0, 3)
(C) (1, 0, 0, 0,3) (D) (1, 0, 0, 0, 0, 3)​

Answer 1

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TO CHOOSE THE CORRECT OPTION

The coefficient form of the polynomial

$\sf{ {y}^{5} + 3\: }$

(A) (1, 3)

(B) (1, 0, 3)

(C) (1, 0, 0, 0,3)

(D) (1, 0, 0, 0, 0, 3)

DEFINITION TO BE MEMORISED

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

CALCULATION

Here the given polynomial is

$\sf{ {y}^{5} + 3 \: }$

Which can be rewritten as

$\sf{ {y}^{5} + 0. {y}^{4} + 0. {y}^{3} + + 0. {y}^{2} + 0.y + 3 \: }$

Hence the the coefficient form of the given polynomial is ( 1 , 0 , 0 , 0 , 0 , 3 )

RESULT

Hence the correct option is

(D) ( 1 , 0 , 0 , 0 , 0 , 3 )

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LEARN MORE FROM BRAINLY

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Answer 2

Given:

A polynomial of degree 5 = $x^{5} + 3$

To Find:

Coefficients of the polynomial =?

Step-by-step explanation:

We know the standard equation of a 5-degree polynomial is $ax^{5} + bx^{4} +cx^{3} + dx^{2} + ex + f$    ............(1)

where a, b, c, d, e, and f are coefficients.

Given the 5-degree equation is $x^{5} + 3$ .............(2)

Now, compare equation (1) and (2)

a = 1 , b = 0, c = 0, d = 0, e =0, f = 3 (These are the coefficients)

Hence, the coefficients of the polynomial $x^{5} + 3$ are (1, 0, 0, 0, 0, 3)  option (D)