Please explain
One factor of x3 + 5x2 + 2x - 8 is (x + 4). Find the remaining factors.
perform either synthetic division or long algebraic division of
(x^3 + 5x^2 + 2x - 8) by (x+4) to get
(x^3 + 5x^2 + 2x - 8) = (x+4)(x^2 + x - 2)
I will leave it up to your to further factor the quadratic, it comes apart very easily.
To find the remaining factors of the polynomial x^3 + 5x^2 + 2x - 8, we can use the polynomial division method.
Step 1: Write the polynomial in descending order of powers:
x^3 + 5x^2 + 2x - 8
Step 2: Identify the factor we already know, which is (x + 4). We can use this factor to perform polynomial division.
x^2 - x - 2
______________________
(x + 4) | x^3 + 5x^2 + 2x - 8
- (x^3 + 4x^2)
______________________
x^2 + 2x - 8
- (x^2 + 4x)
______________________
-2x - 8
+ (2x + 8)
______________________
0
Step 3: The remainder is equal to 0, which means that (x + 4) is a factor of the polynomial x^3 + 5x^2 + 2x - 8.
Step 4: Write the result of the division in factored form:
x^3 + 5x^2 + 2x - 8 = (x + 4)(x^2 - x - 2)
So the remaining factors of the polynomial are (x^2 - x - 2).