Question

*If polynomial (2a + 3 ) is multiplied by (2a² + 5a + 3 ) then the degree of the answer?*

1️⃣ 1
2️⃣ 2
3️⃣ 4
4️⃣ 3​

Answer 1

Given:

The polynomial (2a +3) is multiplied by (2a² + 5a + 3 ).

To find:

The degree of the answer.

Solution:

First let us multiply the given terms:

=(2a + 3)×(2a² + 5a + 3 )

= 2a(2a² + 5a + 3 ) + 3(2a² + 5a + 3 )

$4 {a}^{3} + 10 {a}^{2} + 6a + 6 {a}^{2} + 15a + 6$

$4 {a}^{3} + 16 {a}^{2} + 21a + 6$

From the expression we can see that the degree of the polynomial is 3.

Therefore the degree of the answer that we receive on multiplying the given expressions is 3, thus the correct option is 4.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If polynomial (2a + 3 ) is multiplied by (2a² + 5a + 3 ) then the degree of the answer

1. 1

2. 2

3. 4

4. 3

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

METHOD TO FIND DEGREE OF PRODUCT OF TWO POLYNOMIALS

If f(x) is a polynomial of degree m and g(x) is a polynomial of degree n then

$\sf{Degree \: of \: f(x).g(x) = Degree \: of \: f(x) + Degree \: of \: g(x) }$

EVALUATION

Here we have to find the degree of the polynomial obtained by multiplying the polynomials (2a + 3 ) and (2a² + 5a + 3 )

Let f(a) = 2a + 3

g(a) = 2a² + 5a + 3

So degree of f(a) = 1 & Degree of g(a) = 2

Hence the required degree of polynomial obtained by multiplying the polynomials (2a + 3 ) and (2a² + 5a + 3 )

$\sf{ = Degree \: of \: \: \: f(a).g(a) }$

$\sf{= Degree \: of \: f(a) + Degree \: of \: g(a) }$

$= 1 + 2$

$= 3$

FINAL ANSWER

Hence the correct option is 4. 3

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