(complexity) The set or property of problems for which no polynomial-time algorithm is known. This includes problems for which the only known algorithms require a number of steps which increases exponentially with the size of the problem, and those for which no algorithm at all is known.

3×2 – 2x-2 is not a polynomial because it has a negative exponent. is not a polynomial because it has a variable under the square root. is not a polynomial because it has a variable in the denominator of a fraction.

Polynomials can be classified by the degree of the polynomial. The degree of a polynomial is the degree of its highest degree term. So the degree of 2×3+3×2+8x+5 2 x 3 + 3 x 2 + 8 x + 5 is 3. A polynomial is said to be written in standard form when the terms are arranged from the highest degree to the lowest degree.

Polynomials are of different types. Namely, Monomial, Binomial, and Trinomial.

Polynomials are even used in various fields of science , such as physics , where we measure acceleration , or to express units of energy , inertia , or even in electricity . etc . In chemistry , polynomials are used in writing down the chemical equations .

For example, an engineer designing a roller coaster would use polynomials to model the curves, while a civil engineer would use polynomials to design roads, buildings and other structures.

Factorization – Exercise 2.2. 2

1. 1) Resolve into factors:
2. (i) x2+xy.
3. (i) a2+ax+ab+bx.
4. (v) (0.7)2-(0.3)2
5. Determine p and q.
6. (ii) 4×2+4x+1.
7. (iii) a2-10a+25.
8. (iv) 2×2-24x+72.

Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly.

enn factorial

Some non-polynomial equations can be solved using polynomial equations. As an example let us consider the equation √(15-2x) = x. First we note that this is not a polynomial equation. Squaring both sides, we get x2 + 2x −15 = 0 .

Degree of a Polynomial

1. b2 −4ac < 0 There are no real roots. 2. b2 −4ac = 0 There is one real root.

one solution

The coefficient of the quadratic term, a, determines how wide or narrow the graphs are, and whether the graph turns upward or downward. A positive quadratic coefficient causes the ends of the parabola to point upward. A negative quadratic coefficient causes the ends of the parabola to point downward.

That’s negative, so there are two complex roots for this equation.

64 is a perfect square number which can be obtained by the square of 8. Hence, the square root of 64 is a rational number….Square Root of 64.