Question

State the degree and dominant term of this polynomial
function. (2 marks)$f(x)=2x(x-3)^3(x+1)(4x-2)$

Answer 1

The degree of the polynomial f(x) = 2x(x - 3)³(x + 1)(4x - 2) is 6, and the dominant term is - 216x²

The degree of the polynomial?

The polynomial function is given as:

f(x) = 2x(x - 3)³(x + 1)(4x - 2)

To determine the degree, we simply add the multiplicities.

So, we have:

Degree = 1 + 3 + 1 + 1

Evaluate

Degree = 6

Hence, the degree of the polynomial is 6

The dominant term of the polynomial

We have:

f(x) = 2x(x - 3)³(x + 1)(4x - 2)

Expand

f(x) = 8x⁶ - 68x⁵ + 176x⁴ - 72x³ - 216x² + 108x

The term with the highest absolute value is - 216x²

Hence, the dominant term is - 216x²

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