Factor x3 4x2 3x + 18 = 0, given that 3 is a zero.
check your typing.
Did you forget any + or - signs between the first 3 terms ?
The way it reads makes no sense.
oh sorry x3-4x2-3x+18=0
Use the ^ sign to indicate exponents
x^3 - 4x^2 - 3x + 18 = 0
since 3 is a root,
then x = 3 , or x-3 is a factor
using either long division or synthetic division,
x^3 - 4x^2 - 3x + 18
(x-3)(x^2 - x - 6) = 0
(x-3)(x-3)(x+2) = 0
so x = 3 or x = -2
thank you this make way more since now
To factor the given equation, we can use synthetic division and the Factor Theorem.
Step 1: Use synthetic division to divide the equation by (x - 3).
3 | 1 4 3 18
------------------
| 3 21 72
------------------
1 7 24 90
The result of the synthetic division is 1 7 24 90.
Step 2: Write the original equation as a product of two factors using the output of the synthetic division.
The equation can be factored as:
(x - 3)(x^2 + 7x + 24) = 0
Now, we need to factor the quadratic equation x^2 + 7x + 24.
Step 3: Factor the quadratic equation.
Since the quadratic equation has no common factors and doesn't easily factor, we can use the quadratic formula to find the solutions.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation x^2 + 7x + 24 = 0, the coefficients are:
a = 1, b = 7, c = 24
Using the quadratic formula, we have:
x = (-7 ± √(7^2 - 4(1)(24))) / (2(1))
x = (-7 ± √(49 - 96)) / 2
x = (-7 ± √(-47)) / 2
Since the expression under the square root is negative, the quadratic equation has no real solutions.
Therefore, the factored form of the equation x^3 + 4x^2 + 3x + 18 = 0, given that 3 is a zero, is:
(x - 3)(x^2 + 7x + 24) = 0