Question

what is the maximum number of terms a fourth-degree polynomial function in standard form can have?

Answer 1

The maximum number of terms fourth-degree polynomial function in standard form can have is 5

The general form of an nth degree polynomial is:

$p(x) = a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2} + ....+a_1x+a_0$

The maximum number of terms that an nth -degree polynomial can have is n+1

For a fourth degree polynomial, n = 4

Substitute n = 4 into $p(x) = a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2} + ....+a_1x+a_0$

$p(x) = a_4x^{4}+a_{4-1}x^{4-1}+a_{4-2}x^{4-2}+a_{4-3}x^{4-3}+a_{4-4}x^{4-4}\\\\p(x) = a_4x^4+a_3x^3+a_2x^2+a_1x+a_0$

The maximum number of terms of p(x) above, when n = 4 is (4+1)

The maximum number of terms fourth-degree polynomial function in standard form can have is 5

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