Cubic Polynomials (Grade 12 NSC Matric Mathematics): Flashcards

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Cubic Polynomials
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Definition of a cubic polynomial

A polynomial where the highest power of the variable is 3

General form of cubic polynomial

y=ax3+bx2+cx+dy = ax^3 + bx^2 + cx + d where a≠0a \neq 0

Degree of a cubic polynomial

3

Polynomial division algorithm formula

a(x)=b(x)×Q(x)+R(x)a(x) = b(x) \times Q(x) + R(x)

Four terms in the division algorithm

Dividend, divisor, quotient, remainder

Leading coefficient in ax3+bx2+cx+dax^3 + bx^2 + cx + d

aa

Three methods for factoring cubic polynomials

Long division, synthetic division, inspection

When synthetic division works

For linear divisors with leading coefficient 1

What synthetic division uses instead of full polynomials

Coefficients only

Operation used in synthetic division

Addition (not subtraction)

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