Solve each of the following equations?

x³ + 5x² = 6x

x = 0, 1 and -6

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x² - 3x = 10

x = 5, -2

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x(x - 2)(x + 3) = 0

x = 0, 2, -3

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I didn't show the working out. I just used my calculator but to get the answer, you can factorise it - it's not too hard. Alternatively, use the quadratic formula (for quadratic equations!)

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assuming that V is a typo you would add the x's and have 4x+1=9 then you subtract 1 from both sides and have 4x=8 then divide both sides by 4 and have x=2 3x+1+x=9 4x+1=9 4x=8 x=2

1)
x^3 + 5x^2 = 6x
x^3 + 5x^2 - 6x = 0
x(x^2 + 5x - 6) = 0
x(x + 6)(x - 1) = 0

x = 0

x + 6 = 0
x = -6

x - 1 = 0
x = 1

∴ x = -6 , 0 , 1

= = = = = = = =

2)
x^2 - 3x = 10
x^2 - 3x - 10 = 0
x^2 + 2x - 5x - 10 = 0
(x^2 + 2x) - (5x + 10) = 0
x(x + 2) - 5(x + 2) = 0
(x + 2)(x - 5) = 0

x + 2 = 0
x = -2

x - 5 = 0
x = 5

∴ x = -2 , 5

= = = = = = = =

3)
x(x - 2)(x + 3) = 0

x = 0

x - 2 = 0
x = 2

x + 3 = 0
x = -3

∴ x = -3 , 0 , 2

x^3+5x^2-6x=0 x(x^2+5x-6)=0 x(x+6)(x-1)=0 x=0,-6,or1

x^2-3x-10=0 (x-5)(x+2)=0 x= 5 or -2

x(x-2)(x+3)=0 x=2,0,or -3 x(x^2+x-6)= x^3+x^2-6x

Question 1
x³ + 5x² - 6x = 0
x (x² + 5x - 6) = 0
x (x + 6)(x - 1) = 0
x = 0 , x = - 6 , x = 1

Question 2
x² - 3x - 10 = 0
(x - 5)(x + 2) = 0
x = 5 , x = - 2

Question 3
x = 0 , x = 2 , x = - 3

x^3+5x^2=6x
x(x² + 5x -6) = 0
x(x +6)(x -1) = 0
x = 0
x = -6
x = 1
---------------------------
x^2-3x=10
x² - 3x - 10
(x -5)(x + 2) = 0
x = 5
x = -2
---------------------------
x(x-2)(x+3)=0
x = 0
x = 2
x = -3