# Atge 4

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ALGEBRA ALGEBRA p (x2 ) + =- Examples : (7 + 5x), (x - 7y), (5x+y + 3yz) are all = (x4 - 5x + 3x + 9) - (2x4 - 3x3 + 5x – 4) binomials. (x4 - 5x2 + 3x + 9) + (- 2x4 + 3x3 – 5x + 4) (iii) Trinomial : A polynomial containing three - (x4 - 2x4) + (-5x2 + 3x) + (3x - 5x) + (9 + 4) nonzero terms is called a trinomial. => x^ - 2x - 2x+ 13 Examples : For the sake of convenience, (8 + 5x + xº), 3x - 5xy + 7y are all trinomials. = x 5x + 3x + 9 Constant Polynomial q(x) = 2x4 3x3 + 5x - 4 A polynomial containing one term only, consist- + ing of a constant is called a constant polynomial. Examples : .. p(x) - 9(x) = - 2x3 - 2x + 13 7 Multiplication Of Two Polynomials 7,-5, etc. are all constant polynomials. 9 To determine the product of two polynomials, the distributive law of multiplication is used first and then Clearly, the degree of a non-zero constant polyno- grouping is made of terms of same degrees for addition mial is zero. and subtraction. Zero Polynomial x2 - 6x + x + 1 A polynomial consisting of one term, namely zero only, is called a zero polynomial. The degree of a zero x2-3x + 2 polynomial is not defined. 6x + x + x2 Zeros Of A Polynomial 3x4 + 18x3 - 3x2 - 3x Let p(x) be a polynomial. If pla) = 0, then we say - 12x + 2x + 2 that a is a zero of the polynomial p(x). Finding the zeros of a polynomial p(x) means solving the equation - 9X4 + 21x3 – 14x2 - x + 2 p(x) = 0. Remember : (-x) * (-x) = + x2 Example : If ſo = 32 - 10t + 6, find fo). (+x) x (-x) = - x Solution : f(t) = 3ť – 10t + 6 (x) x (x) = xe etc. = f(0) = 3 x 02 – 10 x 0 + 6 = 6 samne. If na_22 Or. AX(-) = + 1 జన్ + 2x3 - کد = findo ...
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