Question

Determine the degree of the polynomial. $ (3x - 2)(2{x^3} + 3{x^2}) $

Answer 1

Hint: First of all we will open the brackets and will make the polynomial simplifying the terms after opening the brackets and then will find the degree of the polynomial. Remember Degree is the highest power on its variable.

Complete step-by-step answer:
Take the given polynomial –
 $ (3x - 2)(2{x^3} + 3{x^2}) $
Open the brackets-
 $ = 3x(2{x^3} + 3{x^2}) - 2(2{x^3} + 3{x^2}) $
Remember when you open the brackets and there is a positive sign outside the bracket then there is no change in the sign of the terms inside the bracket but when there is a negative sign outside the bracket then all the terms inside the bracket changes. Positive term becomes negative and negative term becomes positive.
 $ = 3x(2{x^3}) + 3x(3{x^2}) - (2)(2{x^3}) - (2)(3{x^2}) $
Now using the law of power and exponents, when bases are the same then powers are added in case when two powers and exponents have multiplicative sign in between. Also, constants are multiplied directly.
 $ = 6{x^4} + 9{x^3} - 4{x^3} - 6{x^2} $
Check for the like terms and make the pair of it.
 $ = 6{x^4} + \underline {9{x^3} - 4{x^3}} - 6{x^2} $
Simplify the like terms and write other terms as it is –
 $ = 6{x^4} + 5{x^3} - 6{x^2} $
Degree of any polynomial is the highest power or an exponent of its variable.
From the above polynomial it is clear that it is of degree $ 4 $
So, the correct answer is “4”.

Note: know the difference between the degree and order and apply accordingly. In the differential equation, the order is the derivative of the highest order present in the equation. Be very careful about the terms for degree and order. Be careful while you open the brackets and the positive and negative signs of the terms attached therein.