To find the value of ( \frac{6}{x} \cdot 2x^2 ) when ( x = 3 ), first substitute ( x ) with 3. This gives ( \frac{6}{3} \cdot 2(3^2) ). Simplifying, we have ( 2 \cdot 2 \cdot 9 = 36 ). Therefore, the value is 36.
2x2-x-6 = (2x+3)(x-2)
Reading this as: 4x2-6=2x2 This implies that: -6=-2x2 3=x2 x=sqrt(3) and x=-sqrt(3) So x can equal plus or minus the square root of 3
3/(x2+4x-1) = 6/(2x2-3x+5) Cross - multiply in order to eliminate the fractions: 6*(x2+4x-1) = 3*(2x2-3x+5) 6x2+24x-6 = 6x2-9x+15 6x2-6x2+24x+9x = 15+6 33x = 21 x = 21/33 => x = 7/11
2x2 + 6 = 30 is your statement.2x2 = 24x2 = 12x = ±√12x = ±√(4*3)x = 2√3 or x = -2√3
2x + 4 = 6/x - 3 ∴2x - 6/x + 7 = 0 ∴2x2 + 7x - 6 = 0 X ∈ {0.71221447, -4.2122145}
4/6 = (2x2)/(2x3) = 2/3
2x2-x-6 = (2x+3)(x-2)
5/6 - 1/6 = 5-1/6 = 4/6 = 2x2/3x2 = 2/3
Reading this as: 4x2-6=2x2 This implies that: -6=-2x2 3=x2 x=sqrt(3) and x=-sqrt(3) So x can equal plus or minus the square root of 3
2x2-4x-3x+6 2x2-7x+6 (2x+3)(x+2)
3/(x2+4x-1) = 6/(2x2-3x+5) Cross - multiply in order to eliminate the fractions: 6*(x2+4x-1) = 3*(2x2-3x+5) 6x2+24x-6 = 6x2-9x+15 6x2-6x2+24x+9x = 15+6 33x = 21 x = 21/33 => x = 7/11
2x2 + 6 = 30 is your statement.2x2 = 24x2 = 12x = ±√12x = ±√(4*3)x = 2√3 or x = -2√3
2x2 + 7x + 6 = 2x2 + 4x + 3x + 6 = 2x(x + 2) + 3(x + 2) = (x + 2)(2x + 3)
(2x+3)(x-2)
2x + 4 = 6/x - 3 ∴2x - 6/x + 7 = 0 ∴2x2 + 7x - 6 = 0 X ∈ {0.71221447, -4.2122145}
x2+7x=-2x2+6 3x2+7x-6=0 (3x-2)(x+3)=0 3x-2=0 or x+3=0 x=2/3 or x=-3
You would first factor out anything that is common between the 3 parts. 2x2 is the greatest common factor. To pull out the 2x2, you divide each term by 2x2 like so:12x4/2x2=6x210x3/2x2=5x-12x2/2x2=-6We now know that 12x4+10x3-12x2= 2x2(6x2+5x-6)The next step involves using the "slip and slide" method for the trinomial inside the parentheses:6x2+5x-6x2+5x-36(x+9)(x-4)(x+9/6)(x-4/6)(x+3/2)(x-2/3)(2x+3)(3x-2)Remembering that the result for the slip and slide method only accounts for 6x2+5x-6 we must multiply (2x+3)(3x-2) by 2x2.Your final answer is 2x2(2x+3)(3x-2).