leading coefficients

leading coefficients : In mathematics, a coefficient is a constant multiplicative factor of a certain object. For example, in the expression 9 x 2, the coefficient of x 2 is 9. The object can be such things as a variable, a vector, a function, etc. In some cases, the objects and the coefficients are indexed in the same way, leading to expressions such as: where a n is the coefficient of the variable x n for each n = 1, 2, 3, … In a polynomial P( x) of one variable x, the coefficient of x k can be indexed by k, giving the convention that for example: For the largest k where a k ≠ 0, a k is called the leading coefficient of P because most often, polynomials are written starting from the left with the largest power of x. So for example the leading coefficient of the polynomial is 4. The coefficients of polynomial also may be in the other order: and must be a 0 ≠0 and a 0 is the leading coefficient of Q. Important coefficients in mathematics include the binomial..   More from Wikipedia

leading coefficients : In mathematics, the Fibonomial coefficients or Fibonacci-binomial coefficients are defined as where n and k are positive integers and F j is the jth Fibonacci number. The Fibonomial coefficients are all integers...   More from Wikipedia

  This video is an introduction to my method of factoring trinomials. It is similar to others, but mine offers a methodological approach at an easy to understand method. This is the first of two videos focusing on trinomials of the type: ax^2 + bx + c

  This video is an introduction to my method of factoring trinomials. It is similar to others, but mine offers a methodological approach at an easy to understand method. The form is of the trinomial is x^2 + bx + c

Question : Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. P has degree 2, and zeros 1 + i 5 and 1 - i 5. P(x) =?

Answer : If x = a is a zero, then x - a is a factor. Since x = 1 + i 5 and x = 1 - i 5 are solutions, we have the following equation for P(x): P(x) = [x - (1 + i 5)][x - (1 - 5)] ==> P(x) = (x - 1 - i 5)(x - 1 + i 5) You can re-write this and get: P(x) = [(x - 1) + i 5][(x - 1) - i 5] This is a difference of squares, so we can get: P(x) = (x - 1) - (i 5) ==> P(x) = x - 2x + 1 - i (5) ==> P(x) = x - 2x + 1 - (-1)(5) ==> P(x) = x - 2x + 1 + 5 ==> P(x) = x - 2x + 6 Answer Verification: http://www.wolframalpha.com/input/?i=x%C2%B2+-+2x+%2B+6 I hope that helps!..   More from Yahoo Answers

Question : Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. Q has degree 3, and zeros -5 and 1 + i. Q(x) =?

Answer : x^3+ kx^2 + m*x + c (x+5)(x-(1+i))(x-(1-i)) = (x+5)(x^2-x(1+i)-x(1-i)+(1-i^2) = x^3 -2x^2 +2x +5x^2 -10x+ 10 = x^3+3x^2-8x+10 k=3, m=-8, c=10 Q(x)=x^3 + 3x^2 - 8x+ 10..   More from Yahoo Answers

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