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x^2-x-6
Katie
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What property can you use to multiply the expressions with exponents?
The Addition Property of Exponents. To multiply powers with the same base, add the exponents. e.g. 34 x 37 = 311, x2x3 = x5, and (3x2yz3)(2x5y2z) = 6x7y3z4.
What is the gramataical mean of 4 and 9?
1There is no such thing as a "gramataical" mean. There are 3 basic means, and the chart below should clarify that.Assuming you meant "geometric" mean, we have:nth root of (x1 * x2 * ... * xn) or (x1 * x2 * ... * xn)1/n.Thus, plugging in the values, we have:(4 * 9)1/2 which is a square root, gives the value: sqrt(4 * 9).Distribute (or simply multiply) the values with the square root. So:sqrt(36) = 6, or sqrt(4) * sqrt(9) = 2 * 3 = 6.Means:The 3 basic means are: AM, GM, and HM. AM (Arithmetic Mean):(x1 + x2 + ... + xn)/n = AMAdd all the values, and divide by the number of terms you have.GM (Geometric Mean):(x1 * x2 * ... xn)1/n or nth root of (x1 * x2 * ... * xn)Multiply all the values and take the nth root of thereof.HM (Harmonic Mean):n/(1/x1 + 1/x2 + ... 1/xn). (When dealing with 2 terms, we can use the formula: (2x1x2)/(x1 + x2), and 3 using (3x1x2x3)/(x1x2 + x2x3 + x1x3), satisfying the addition comboniation 1 + 2 = 3).
What is X3 plus X2 plus X plus 1 divided by X-1?
(x3 + x2 + x + 1)/(x -1) (using the long division)x2(x - 1) = x3 - x2x3 + x2 + x + 1 - (x3 - x2) = 2x2 + x + 12x(x - 1) = 2x2 - 2x2x2 + x + 1 - (2x2 - 2x) = 3x + 13(x - 1) = 3x - 33x + 1 - (3x - 3) = 4 (the remainder)(x3 + x2 + x + 1)/(x -1) = x2 + 2x + 3 + 4/(x -1)(1x3 + 1x2 + 1x + 1)/(x -1) (using the synthetic division)(the constant of the divisor) 1] 1 1 1 1 (the coefficients of the dividend)The coefficients of the quotient:11 + 1*1 = 21 + 2*1 = 3Since the degree of the first term of the quotient is one less than the degree of the first term of the dividend, the quotient is x2 + 2x + 3.The remainder1 + 3*1 = 4(x3 + x2 + x + 1)/(x -1) = x2 + 2x + 3 + 4/(x -1)
