Question

(x – 2) and (x + 2) are the factors of x³ + x² – 4x – 4. The third factor of the given polynomial is ______.

विकल्प

• (x – 1)

• (x – 4)

• (x + 1)

• (x + 4)

Answer 1

(x – 2) and (x + 2) are the factors of x³ + x² – 4x – 4. The third factor of the given polynomial is (x + 1).

Explanation:

Given, (x – 2) and (x + 2) are the factors of x³ + x² – 4x – 4.

⇒ (x – 2)(x + 2) = x² – 4

Thus, x² – 4 is also the factor of x³ + x² – 4x – 4.

                x + 1
`x^2 - 4")"overline(  x^3 + x^2 - 4x - 4)`
          + x³  – 4x
            –      +                      
                               x²  –  4
                             +x² –  4
                             –     +     
                                0

Thus, x³ + x² – 4x – 4 = (x² – 4)(x + 1)

= (x + 2)(x – 2)(x + 1)