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Simplify by dividing x3 plus 2x2 plus 3x-6 over x-1?
(x^3 + 2x^2 + 3x - 6)/(x - 1) add and subtract x^2, and write -6 as (- 3) + (-3) = (x^3 - x^2 + x^2 + 2x^2 - 3 + 3x - 3)/(x - 1) = [(x^3 - x^2) + (3x^2 - 3) + (3x - 3)]/(x - 1) = [x^2(x - 1) + 3(x^2 - 1) + 3(x - 1)]/(x - 1) = [x^2(x - 1) + 3(x - 1)(x + 1) + 3(x - 1)]/(x - 1) = [(x - 1)(x^2 + 3x + 3 + 3)]/(x - 1) = x^2 + 3x + 6
Solve simultaneously y equals 2-x and x2 plus 2xy equals 3?
if y = 2- x then x^2 + 2x(2 - x) = 3 ie x^2 + 4 x -2x^2 = 3 ie 4x - 3 = x^2 x^2 - 4x +3 = 0 = (x - 1)(x - 3) so x = 1 or 3 Check: y= 2 - 1 =1; x^2 = 1, 2xy = 2 x 1 x 1 = 2, 1 +2 = 3. y = 2 - 3 = -1; x^2 = 9, 2xy = 2 x 3 x -1 = -6, 9 + -6 = 3. QED.
What is three fourths of four fifths?
3/4 x 4/5 = 12/20 = 6/10 = 3/5 or three fifthsNotice that the fours cancel out. Think about writing it as:3 x (1/4) x 4 x (1/5) = 3 x [(1/4) x 4] x (1/5) = 3 x [1] x (1/5) = 3 x (1/5) = 3/5.
How do you factor x squared plus 4x plus 3?
x2 + 4x + 3 =(x + 3) (x + 1)
What is the solution of x2 plus x plus 1 equals 0?
x2 + x + 1 = 0 ∴ x2 + x + 1/4 = -3/4 ∴ (x + 1/2)2 = -3/4 ∴ x + 1/2 = ± √(-3/4) ∴ x = - 1/2 ± (i√3) / 2 ∴ x = (-1 ± i√3) / 2
