Answer:
Option (4)
Explanation:
Given polynomial is,
P(x) = 1x³ - 7x² + 2x + 40
If (x - 5) is a factor of the given polynomial,
Synthetic division by x = 5,
5 | 1 -7 2 40
<u> ↓ 5 -10 -40</u>
1 -2 -8 0
Therefore, factored form of the polynomial will be,
P(x) = (x - 5)(x²- 2x - 8)
Now we further factorize the expression (x² - 2x - 8),
(x² - 2x - 8) = x²- 4x + 2x - 8
= x(x - 4) + 2(x - 4)
= (x + 2)(x - 4)
Now fully factored form of the polynomial will be,
P(x) = (x - 5)(x + 2)(x - 4)
Therefore, remaining factors of the polynomial other than (x - 5) are (x - 4)(x + 2)
Option (4) will be the correct option.
