Question

If x²-4 is a factor of polynomial x³+x² - 4x-4, then its factors are​

Answer 1

Answer:

x^3-4x+x^2-4

x(x^2-4)+(x^2-4)

(x+1)(x^2-4)

(x+1)(x+2)(x-2)

Answer 2

If x²- 4 is a factor of polynomial x³ + x² - 4x - 4 then its factors are ( x + 2 ) ( x - 2 ) ( x + 1 )

Given :

• The polynomial x³ + x² - 4x - 4
• x² - 4 is a factor of polynomial x³ + x² - 4x - 4

To find :

The factors

Solution :

Step 1 of 3 :

Write down the given polynomial

The polynomial is

x³ + x² - 4x - 4

Step 2 of 3 :

Factorise the polynomial

$\sf {x}^{3} + {x}^{2} - 4x - 4$

$\sf = {x}^{2}(x + 1) - 4(x + 1)$

$\sf =( {x}^{2} - 4)(x + 1)$

$\sf =( {x}^{2} - {2}^{2} )(x + 1)$

$\sf =(x + 2)(x - 2)(x + 1)$

Step 3 of 3 :

Find all factors

x² - 4 = ( x + 2 ) ( x - 2 )

Since it is given that x²- 4 is a factor of polynomial x³ + x² - 4x - 4

So the remaining factor is x + 1

All factors are ( x + 2 ) ( x - 2 ) ( x + 1 )

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