Answer:
see explanation
Step-by-step explanation:
Using the coefficients of the polynomial and evaluating for h = - 3
- 3 | 1 - 4 - 9 36
↓ - 3 21 - 36
-------------------------
1 - 7 12 0 ← remainder
Since remainder is 0 then (x + 3) is a factor, so
y = (x + 3)(x² - 7x + 12)
To factor the quadratic
Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (- 7)
The factors are - 4 and - 3, since
- 4 × - 3 = + 12 and - 4 - 3 = - 7, then
x² - 7x + 12 = (x - 4)(x - 3), and
y = (x + 3)(x - 4)(x - 3)
