How do you factor given that #f(8)=0# and #f(x)=x^3-11x^2+14x+80#?
1 Answer
Explanation:
Since
Divide the function by
How to perform polynomial division when the divisor is a binomial:
1. Treat each term of the dividend as a "digit". We will performing division by "digit" (similar to number division)
2. Perform division with the first "digit" of the binomial only
3. When multiplying the resulting quotient back with the divisor, include the remaining digit
4. Subtract the resulting product from the dividend
5. Repeat 1-4 with the resulting difference until division is no longer possible
I can't format the polynomial division properly so I will apologize in advance.
<pre>
x^2 - 3x - 10
-------------------------------
x - 8 / x^3 - 11x^2 + 14x + 80
- (x^3 - 8x^2)
--------------
-3x^2 + 14x + 80
-(-3x^2 + 24x)
------------------
-10x + 80
-10x + 80
-------------
0
</pre>
Factor out the quadratic polynomial
List out all the factors of the last term
We need the product to be negative, the factors need to be of different sign.
Take a look at the sign of the middle term
Add the factors, the resulting value should be equal to the middle term