Question

What is the correct answer?

Answer 1

Option (4)

Step-by-step 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

↓ 5 -10 -40

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.