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7X^3 Third degree polynomial.
(3x + 4)(2x - 1)
When the given expression equals 0 then x = -1/6 and x = -6
6x2 + 13x + 2 = (6x + 1)(x + 2).
x3 - 6x2 + 7x - 2 = x3 - x2 - 5x2 + 5x + 2x - 2 = x2(x - 1) - 5x(x - 1) + 2(x - 1) = (x - 1)(x2 - 5x + 2) = (x - 1){x - 0.5*[5 - sqrt(25 - 8)]}){x + 0.5*[5 - sqrt(25 - 8)]} = (x - 1)(x - 0.4384)(x - 4.5616) so that the roots are x = 1 x = 0.4384 and x = 4.5616
7X^3 Third degree polynomial.
(3x + 4)(2x - 1)
The polynomial 7x3 + 6x2 - 2 has a degree of 3, making it cubic.
6x2 + 11x + 3 = 6x2 + 9x + 2x + 3 = 3x(2x + 3) + 1(2x + 3) = (2x + 3)(3x + 1)
x3 - 6x2 + 4x + 15 = (x - 3)(x - (3/2 + √29/2))(x - (3/2 - √29/2)) ⇒ roots are x = 3, x = 3/2 + √29/2 (≈ 4.19), or x = 3/2 - √29/2 (≈ -1.19)
When the given expression equals 0 then x = -1/6 and x = -6
6x2 + 13x + 2 = (6x + 1)(x + 2).
x3 - 6x2 + 7x - 2 = x3 - x2 - 5x2 + 5x + 2x - 2 = x2(x - 1) - 5x(x - 1) + 2(x - 1) = (x - 1)(x2 - 5x + 2) = (x - 1){x - 0.5*[5 - sqrt(25 - 8)]}){x + 0.5*[5 - sqrt(25 - 8)]} = (x - 1)(x - 0.4384)(x - 4.5616) so that the roots are x = 1 x = 0.4384 and x = 4.5616
6x2-2x+36 = 5x2+10x 6x2-5x2-2x-10x+36 = 0 x2-12x+36 = 0 (x-6)(x-6) = 0 x = 6 or x = 6 It has two equal roots.
Divide all terms by 3:- 2x2+5x-3 = (2x-1)(x+3) when factored
9+6x2=21
-6x2 + 3x - 4 can be factored into (-x + 4)(x + 1). This equals 0 only when x is either 4 or -1. Therefore, the latter two numbers are both roots of the given function.