Online Linear, Quadratic, Cubic Polynomials Homework Help
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DEGREE OF A POLYNOMIAL:
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.
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
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.
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.
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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