Solve by factoring x^3-4x^2-3x+18=0
You would factor by grouping
I tried it didn't work
Man, you're a better grouper than I am. The 18 made me think of 9*2, so I got
x(x-3)^2 = x^3-6x^2+9x
hmm. too many x^2, so
2(x-3)^2 = 2x^2-12x+18
aha - (x+2)(x-3)^2
I see, for this problem you would have to plug in numbers with trial and error, by doing this you get x=-2 as one of the roots, then you would factor (x+2)out of the problem. Then you would get x²-6x+9. This is a perfect square, so when you factor that, you get (x-3)^2.
So you would get (x+2)(x-3)^2
ok thanks for your help:D
To solve the equation x^3 - 4x^2 - 3x + 18 = 0 by factoring, you can follow these steps:
Step 1: Group the terms.
Rearrange the equation by grouping the terms together:
(x^3 - 4x^2) + (- 3x + 18) = 0
Step 2: Factor out common terms.
Factor out the greatest common factor from each group:
x^2(x - 4) - 3(x - 6) = 0
Step 3: Factor by grouping.
Now, look for common factors within each group:
x^2(x - 4) - 3(x - 6) = 0
x(x - 4)(x - 6) - 3(x - 6) = 0
Step 4: Combine like terms.
Combine the terms within each group:
(x - 4)(x^2 - 6x) - 3(x - 6) = 0
Step 5: Factor out common factors.
Factor out the common factors from each group:
(x - 4)x(x - 6) - 3(x - 6) = 0
Step 6: Simplify and solve.
Combine like terms and set the equation equal to zero:
(x - 4)(x(x - 6) - 3) = 0
Now, you have a product of two factors equaling zero. According to the zero product property, if a product of factors equals zero, then at least one of the factors must equal zero. So, set each factor equal to zero and solve for x:
x - 4 = 0 -> x = 4
x(x - 6) - 3 = 0 -> x^2 - 6x - 3 = 0
To solve the second equation, we can use the quadratic formula or factoring as well. However, I will provide the solutions using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Using the quadratic formula, with a = 1, b = -6, and c = -3, we can solve for x:
x = (6 ± √((-6)^2 - 4(1)(-3))) / (2(1))
x = (6 ± √(36 + 12)) / 2
x = (6 ± √48) / 2
x = (6 ± √(16 * 3)) / 2
x = (6 ± 4√3) / 2
x = (3 ± 2√3)
So, the solutions to the equation x^3 - 4x^2 - 3x + 18 = 0 are:
x = 4,
x = 3 + 2√3,
x = 3 - 2√3.