Question

If $A = \left( {3x + 6} \right)$ and $B = 2{x^2} + 3x + 6$, then degree of AB is
A) 4
B) 3
C) 2
D) 1

Answer 1

Hint:
Here, the given question refers to the concept of degree i.e. the maximum power.
To find the answer for this, 1st we will multiply A and B. After it the maximum power of the polynomial will be our required answer.

Complete step by step solution:
it is given in the question that $A = \left( {3x + 6} \right)$ and $B = 2{x^2} + 3x + 6$
Then, we have to find the degree of AB.
Since, $A = \left( {3x + 6} \right)$ and $B = 2{x^2} + 3x + 6$
Now,
  $ = AB\left( {3x + 6} \right)\left( {2{x^2} + 3x + 6} \right)$
  $AB = 6{x^3} + 9{x^2} + 12x + 12{x^2} + 18x + 24$
 $AB = 6{x^3} + 21{x^2} + 30x + + 24$
From, the above equation it is clear that highest power of x is 3

Therefore, the degree of function AB is 3.

Note:
Degree: Degree of the function can be defined as the highest power of the variable.
Types of equation as per degree:
The equation with degree 1 is called linear equation.
For example: In equation $ax + b$ , the degree of variable x is 1.
The equation with degree 2 is called quadratic equation.
For example: In equation $a{x^2} + bx + c$ , the degree of variable x is 2.
The equation with degree 3 is called the cubic equation.
For example: In equation $a{x^3} + b{x^2} + cx + d$ , the degree of variable x is 3.
The equation with degree 4 is called a biquadratic equation.
For example: In equation $a{x^4} + b{x^3} + c{x^2} + dx + e$ , the degree of variable x is 4.