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Degree Of Polynomials

Types of Polynomials Assignment / Homework Help
The highest power of the variable in a polynomial is known as the degree of the polynomial.

For example, the degree of the polynomial 4x7 2x6 + x + c is 7 and the degree of the polynomial 7y6 3y2 4 is 6.


POLYNOMIALS OF DIFFERENT DEGREES:

LINEAR POLYNOMIAL:

A polynomial whose degree is 1 is named as a linear polynomial. Any linear polynomial is of the form ax + b, where x is a variable and a, b are constants. Also a ≠ 0 (because if a = 0, then the polynomial will become 0 + b = b which is a constant polynomial of 0 degree.)

Examples:

p(x) = 3x + 2
q(x) = 4y
r(z) = z + √2
s(t) = 5 t


QUADRATIC POLYNOMIAL:

A polynomial with degree 2 is known as a quadratic polynomial. Any quadratic polynomial in one variable x is of the form ax2 + bx + c, where a, b, c are constants. Also a ≠ 0 (because if a = 0, then the polynomial will become 0 + bx + c = bx + c which is a linear polynomial of degree 1).

Examples:

4 x x2, 3 x2, 2x + 3x2 etc. are some examples of quadratic polynomials.


CUBIC POLYNOMIAL:

A polynomial whose degree is 3 is termed as a cubic polynomial. Hence any cubic polynomial in one variable x is of the form ax3 + bx2 + cx + d, where a, b, c and d are constants and a ≠ 0 (because if a = 0, then the polynomial will be 0 + bx2 + cx + d = bx2 + cx + d which is a quadratic polynomial of degree 2).

Examples:

5x3 + x2, x3 + 2x2 + 3x + 5, 2x3, 4 x3, 3x3 x and 4x3 + 3 are a few examples of cubic polynomials.


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