Zeros Of A Polynomial FunctionIf for x = a, the value of the polynomial p(x) is 0 i.e., p(a) = 0; then x = a is a zero of the polynomial p(x).For Example: (i) For polynomial p(x) = x – 2; p(2) = 2 – 2 = 0 ∴ x = 2 or simply 2 is a zero of the polynomial p…

Types Of Polynomials(i) Based on degree : If degree of polynomial isExamples1.One  Linearx + 3, y – x + 2, √3x –32.TwoQuadratic2x2 –7, \(\frac{1}{3}{{\text{x}}^{2}}+{{\text{y}}^{2}}-2\text{xy}\), x2 +1+ 3y3.ThreeCubicx3 + 3x2 –7x+8, 2x2+5x3+7,4.Fourbi-qu…

Algebraic ExpressionAny combination of literal numbers or variables and numbers (numerals) connected by +, –, × or ÷ signs is called an algebraic expression. For example, 5, 6x, a + b × c, 4 × m + n, x – y ÷ z are algebraic expressions. The perimeter P o…

Polynomials In One VariableIf a polynomial has only one variable then it is called polynomial in one variable. P(x) = 2x3 + 5x – 3                            Cubic trinomial Q(x) = 7x7 – 5x5 – 3x3 + x + 3    polynomial of degree 7 R(y) = y              …

Values Of A Polynomial FunctionFor a polynomial f(x) = 3x2 – 4x + 2. Values Of A Polynomial To find its value at x = 3; replace x by 3 everywhere. So, the value of f(x) = 3x2 – 4x + 2 at x = 3 is f(3) = 3 × 32 – 4 × 3 + 2 = 27 – 12 + 2 = 17. Similarly, …

Form A Polynomial With The Given ZerosLet zeros of a quadratic polynomial be α and β. x = β,               x = β x – α = 0,   x ­– β = 0 The obviously the quadratic polynomial is (x – α) (x – β) i.e.,  x2 – (α + β) x + αβ x2 – (Sum of the zeros)x + Prod…

Degree Of A PolynomialThe greatest power (exponent) of the terms of a polynomial is called degree of the polynomial. For example : In polynomial 5x2 – 8x7 + 3x: (i) The power of term 5x2 = 2 (ii) The power of term –8x7 = 7 (iii) The power of 3x = 1 Since…

Remainder TheoremTheorem: Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a).Utilize Remainder Theorem Calculator to get the remai…