Question

Degree of the polynomial (a^2 + 1)(a + 2)( a^3 + 3) is

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Answer 1

Step-by-step explanation:

Given :-

The polynomial (a² + 1)(a + 2)( a³ + 3)

To find :-

Determine the degree of the Polynomial ?

Solution :-

Given polynomial is (a² + 1)(a + 2)( a³ + 3)

=> [(a²+1)(a+2)](a³+3)

=>[a²(a+2)+1(a+2)](a³+3)

=> (a³+2a²+a+2)(a³+3)

=> a³(a³+3)+2a²(a³+3)+a(a³+3)+2(a³+3)

=> a⁶+3a³+2a⁵+6a²+a⁴+3a+2a³+6

=> a⁶+2a⁵+a⁴+5a³+6a²+3a+6

The heighest of all powers of the coefficients is 6

The degree = 6

Short cut:-

Given polynomial is (a² + 1)(a + 2)( a³ + 3)

The variable s are a², a, a³

Their product = a²×a×a³ = a⁶

So , the degree = 6

Answer:-

The degree of the given polynomial is 6

Used formulae:-

The heighest of all powers of the variables of the terms present in the polynomial is the degree of the polynomial.