This equation is a cubic polynomial, meaning it is of the form ax^3 + bx^2 + cx + d = 0.
In this case, the coefficients are:a = 3b = -2c = 1d = -10
To solve this equation, we can use various methods such as factoring, synthetic division, or the cubic formula. Let's try factoring first:
3x^3 - 2x^2 + x - 10 = 0Rearrange the equation:3x^3 - 6x^2 + 4x - 8x^2 + 8x - 10 = 0Group terms:3x^2(x - 2) + 4x(x - 2) - 10 = 0Factor out common terms:(3x^2 + 4x)(x - 2) - 10 = 0Factor further:x(3x + 4)(x - 2) - 10 = 0
Now, set each factor to zero and solve for x:1) x = 02) 3x + 4 = 03x = -4x = -4/33) x - 2 = 0x = 2
Therefore, the solutions to the equation 3x^3 - 2x^2 + x - 10 = 0 are x = 0, x = -4/3, and x = 2.
This equation is a cubic polynomial, meaning it is of the form ax^3 + bx^2 + cx + d = 0.
In this case, the coefficients are:
a = 3
b = -2
c = 1
d = -10
To solve this equation, we can use various methods such as factoring, synthetic division, or the cubic formula. Let's try factoring first:
3x^3 - 2x^2 + x - 10 = 0
Rearrange the equation:
3x^3 - 6x^2 + 4x - 8x^2 + 8x - 10 = 0
Group terms:
3x^2(x - 2) + 4x(x - 2) - 10 = 0
Factor out common terms:
(3x^2 + 4x)(x - 2) - 10 = 0
Factor further:
x(3x + 4)(x - 2) - 10 = 0
Now, set each factor to zero and solve for x:
1) x = 0
2) 3x + 4 = 0
3x = -4
x = -4/3
3) x - 2 = 0
x = 2
Therefore, the solutions to the equation 3x^3 - 2x^2 + x - 10 = 0 are x = 0, x = -4/3, and x = 2.